A square with side length 4 is placed against a square with side length a. The area of the red region is 88/15. Find a.

Guest Dec 11, 2020

#1**0 **

The area of one of the right triangular white regions in the smaller square is

(4^2 - 88/15)/2 = 76/15

So......the other leg , L, of one of these right triangles can be found as

76/15 = (1/2) 4 * L

76/30 = L = 38/15

So the top side of the red region has the length = 4 - 38/15 = [60 -38]/15 = 22/15

And using similar triangles the difference, D, in height between the larger square and the smaller square is

4/(38/15) = D/ ( 22/15)

4/38 = D/22

88 = 38D

88/38 = D

44/19 = D

a = 4 + 44/19 = [76 + 44 ] /19 = 120/19

CPhill Dec 11, 2020