Question

please help me to sort out these squares

Two squares have sides x cm and ( x+ 4 ) cm .The sum of their squares is 656 sq cm .
Find the sides of the squares.

PLEASE FAST

Answer 1

Let the side of the smaller square = x cm.

Then the side of the larger square = (x + 4)cm.

Given that sum of their squares = 656 sq.cm.

x^2 + (x + 4)^2 = 656

x^2 + x^2 + 16 + 8x = 656

2x^2 + 8x = 656 - 16

2x^2 + 8x = 640

2x^2 + 8x - 640 = 0

x^2 + 4x - 320 = 0

x^2 + 20x - 16x - 320 = 0

x(x + 20) - 16(x + 20) = 0

(x + 20)(x - 16) = 0

x + 20 = 0 (or) x - 16 = 0

x = -20, x = 16.

Since x cannot be -ve, so x = 16

Hence,

The side of the smaller square = 16cm.

Side of the larger square = x + 4

                                          = 16 + 4

                                          = 20cm.


Sides of the square = 16^2 + 20^2

                                  = 256 + 400

                                  = 656.



Hope this helps!