Problem: Finding the area of a square

Question

I can't post photos here so you can find the photo on imgur.com/a/i24lMmS

I need to find the area of the big square, but i don't know how. I tried to solve but i

can't seem to figure it out.

Any help would be appreciated, thanks!

Answer 1

More information is needed. If I could use the 2 triangles with the formula a^2+b^2=c^2; you'd get an answer.

Answer 2

Here's how I approached the problem. First I disregarded the small 16x16 square. The 37x37 square inside of the larger square makes four congruent triangles, top left, top right, bottom left, and bottom right. There are Pythagorean triples such as 3-4-5, 5-12-13, and so on. So, I tried to find a Pythagorean Triple whose sides are integers and whose hypotenuse is 37. By trial and error I found that 12-35-37 is a Pythagorean Triple.

37^2=12^2+35^2, 1369=144+1225=1369. Therefore, looking at the top two triangles, the top left triangle has a horizontal leg of 35 and a vertical leg of 12. Therefore the top right triangle has a horizontal leg of 12.

Therefore, the top horizontal side of the largest square is 35+12=47. So, all of the sides of the largest square are 47. The area of the largest square is 47x47=2209. To check to see if this is correct, this area must equal the area of the 37x37 square plus the areas of the four congruent triangles. Each triangle has an area of A=(1/2)*12*35=210. The area of the 37x37 square is 1369. 1369+4*210=1369+840=2209 sq units. The area of the largest square is 47X47=2209 sq units. I don't see how the small square fits into the problem.