# Interesting geometry questions. **URL:** \ **Category:** Miscellaneous and Personal Stuff I Must Share\ **Created:** [June 15, 2016, 11:42am UTC](https://boards.straightdope.com/t/interesting-geometry-questions/757411 "2016-06-15T11:42:39Z")\ **Posts on this page:** 12\ **Page:** 2
**Author:** ![Knowed\_Out](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/knowed_out/32/7380_2.png) [@Knowed\_Out](https://boards.straightdope.com/u/Knowed_Out)\ **Post date:** [June 15, 2016, 11:53pm UTC](https://boards.straightdope.com/t/interesting-geometry-questions/757411/21 "2016-06-15T23:53:46Z")
I solved both of them using Algebra, which I don’t think I learned until I was 14. ---
**Author:** ![TriPolar](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tripolar/32/3008_2.png) [@TriPolar](https://boards.straightdope.com/u/TriPolar)\ **Post date:** [June 16, 2016, 12:10am UTC](https://boards.straightdope.com/t/interesting-geometry-questions/757411/22 "2016-06-16T00:10:44Z")
> [@jtur88](#): > > Common sense, without any forumlas or theorems, told me the perimeter remains the same even if you cut out square corners. Like walking to the store, in a city with grid streets. It’s the same distance, whether you go all around the box, or take the intermediate streets in zigzag fashion. > [@Little\_Nemo](#): > > As long as you know the angles are all right angles, it’s easy to “move” the sides around so they form regular rectangles. Then it’s simple addition. This concept told me what it was because I’ve seen similar problems before. ---
**Author:** ![TonySinclair](https://avatars.discourse-cdn.com/v4/letter/t/49beb7/32.png) [@TonySinclair](https://boards.straightdope.com/u/TonySinclair)\ **Post date:** [June 16, 2016, 12:21am UTC](https://boards.straightdope.com/t/interesting-geometry-questions/757411/23 "2016-06-16T00:21:43Z")
> [@Riemann](#): > > The valid criticisms are that the shapes are drawn way off scale; and it’s not clear what measurement the 2cm in the second diagram is indicating (although of course only one is consistent with the problem being solvable). Username checks out. ---
**Author:** ![Richard\_Pearse](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/richard_pearse/32/13144_2.png) [@Richard\_Pearse](https://boards.straightdope.com/u/Richard_Pearse)\ **Post date:** [June 16, 2016, 12:34am UTC](https://boards.straightdope.com/t/interesting-geometry-questions/757411/24 "2016-06-16T00:34:50Z")
> [@Knowed\_Out](#): > > I solved both of them using Algebra, which I don’t think I learned until I was 14. You don’t need algebra though. You can just use the common sense methods described in this thread. ---
**Author:** ![JohnGalt](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/johngalt/32/184_2.png) [@JohnGalt](https://boards.straightdope.com/u/JohnGalt)\ **Post date:** [June 16, 2016, 1:13am UTC](https://boards.straightdope.com/t/interesting-geometry-questions/757411/25 "2016-06-16T01:13:51Z")
Gah! I thought the question was to solve the AREA, not the perimeter. The perimeter was obvious to me. I don’t think you could solve for the area though. ---
**Author:** ![davidm](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/davidm/32/225_2.png) [@davidm](https://boards.straightdope.com/u/davidm)\ **Post date:** [June 16, 2016, 1:16am UTC](https://boards.straightdope.com/t/interesting-geometry-questions/757411/26 "2016-06-16T01:16:47Z")
No, you can’t solve the area with the information given. ---
**Author:** ![zoid](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/zoid/32/336_2.png) [@zoid](https://boards.straightdope.com/u/zoid)\ **Post date:** [June 16, 2016, 2:48am UTC](https://boards.straightdope.com/t/interesting-geometry-questions/757411/27 "2016-06-16T02:48:36Z")
> [@JohnGalt](#): > > Gah! I thought the question was to solve the AREA, not the perimeter. The perimeter was obvious to me. I don’t think you could solve for the area though. Glad I’m not the only one ---
**Author:** ![Joey\_P](https://avatars.discourse-cdn.com/v4/letter/j/919ad9/32.png) [@Joey\_P](https://boards.straightdope.com/u/Joey_P)\ **Post date:** [June 16, 2016, 3:38am UTC](https://boards.straightdope.com/t/interesting-geometry-questions/757411/28 "2016-06-16T03:38:48Z")
> [@JohnGalt](#): > > Gah! I thought the question was to solve the AREA, not the perimeter. The perimeter was obvious to me. I don’t think you could solve for the area though. That was my problem too. I was just about to point out a fatal flaw in treis’ solution because it made an assumption that you can’t make (if one were trying to find the area). Finding the perimeter, however, I could see 5th graders working on this, especially if it was a bonus question, or at least one that was known to be harder. This almost segues transverse lines (go with me on this). I remember struggling with those in grade school. Trying to remember which angles were the same, which ones were opposite and so on. Then one day I realized that you could take the two parallel lines and _slide_ them together (in your head, anyways) and the acted like a single angle, at least WRT which angles were the same, opposite etc. That goes with what Little Nemo was saying about being able to slide the edge in and out, if you can problem solve that in your head, that’s kind of what math is about. Having said that, IMO, that’s not really what you want to do here. I’m guessing the point of this exercise was to learn that two unknown vertical parts add up to 12 and the two unknown horizontal parts add up to 10. What you can do with that knowledge is limited, but you can find the perimeter with it. ---
**Author:** ![davidm](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/davidm/32/225_2.png) [@davidm](https://boards.straightdope.com/u/davidm)\ **Post date:** [June 16, 2016, 4:03am UTC](https://boards.straightdope.com/t/interesting-geometry-questions/757411/29 "2016-06-16T04:03:42Z")
I solved the first one in my mind by sliding the right hand vertical line out so as to make a rectangle, and then realizing that this created a gap at the top that was the same length as the horizontal width of the small extension. I solved the second one similarly by realizing that it was the same as a 9 by 11 rectangle except that the two 2cm horizontals added 4cm to the length. ---
**Author:** ![octopus](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/octopus/32/3716_2.png) [@octopus](https://boards.straightdope.com/u/octopus)\ **Post date:** [June 16, 2016, 4:56am UTC](https://boards.straightdope.com/t/interesting-geometry-questions/757411/30 "2016-06-16T04:56:02Z")
> [@davidm](#): > > Scroll down to the second image to see both questions. > > [Can you solve this 'impossible' maths question aimed at ten-year-old pupils? - Manchester Evening News](http://www.manchestereveningnews.co.uk/news/greater-manchester-news/can-you-solve-impossible-maths-11437050) > > These questions were supposedly given to 10 year old students and baffled their college educated parents. > > A lot of people have been saying it’s unsolvable but it’s not. Many are saying that the answers are 44 for the first question and also 44 for the second.The second problem is ambiguous and the answer assumes that the 2cm label refers to the vertical line to its left. It seems to me that this must be true or it wouldn’t be solvable. > > I couldn’t understand how these two answers could be correct but after several minutes I understood that they are in fact the correct answers. > > I’ll add that I at first thought that it depended on the drawings being in correct proportion. In other words, it could only be solved for the first drawing by physically measuring the image to determine the size of the small box in relation to the larger box and similarly for the second. This is wrong. The solution does not require measuring the images or that the drawings be in correct proportion. It took me several minutes to realize this. > > I would hope that the principles involved here had been taught in class, otherwise it seems a little advanced for 10 year olds. Tricky problem. Took me a minute to puzzle it out. But then it became obvious. being rectilinear is one clue. Realizing that breaking a line segment into multiple line segments doesn’t change their total length is the second clue. ---
**Author:** ![Richard\_Pearse](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/richard_pearse/32/13144_2.png) [@Richard\_Pearse](https://boards.straightdope.com/u/Richard_Pearse)\ **Post date:** [June 16, 2016, 5:00am UTC](https://boards.straightdope.com/t/interesting-geometry-questions/757411/31 "2016-06-16T05:00:31Z")
> [@JohnGalt](#): > > Gah! I thought the question was to solve the AREA, not the perimeter. The perimeter was obvious to me. I don’t think you could solve for the area though. I did the same. A good case of RTFQ. ---
**Author:** ![TriPolar](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tripolar/32/3008_2.png) [@TriPolar](https://boards.straightdope.com/u/TriPolar)\ **Post date:** [June 16, 2016, 1:13pm UTC](https://boards.straightdope.com/t/interesting-geometry-questions/757411/32 "2016-06-16T13:13:31Z")
> [@zoid](#): > > Glad I’m not the only one At first glance the area thing through me off, but I just recently did some things that reminded how little area and perimeter are related in geometric shapes. [Previous page](https://boards.straightdope.com/t/interesting-geometry-questions/757411.md?page=1)