Question

The difference of perimeter of two squares 32 metre and difference of their areas is 208m2.(a) what is the difference between the lengths of their sides
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Answer 1

Answer:

x22 - y22 = 208

Same as:

(x + y)(x - y) = 208 (1)

4x - 4y = 32

x = (32 + 4y)/4 ===> x = 8 + y

Sub. x = 8 + y into equation (1)

(8 + y + y)(8 + y - y) = 208 ===> ( 8 + 2y)(8) = 208 ==> 64 + 16y = 208===> 16y = 144 ===> y = 9

Sub 9 for y into equation (1)

(x + 9)(x - 9) = 208===> x22 - 81 = 208===> x22 = 289 ==>x = +/- 17

We can not have a -side so x = + 17 is chosen.

The difference between their sides is 17 - 9 = 8 meters

Answer is: 8 meters