Question

PLEASE ANSWER THIS QUESTION AS FAST AS POSSIBLE !!!!!!!
Sum of the areas of two squares is 400 cm square. If the difference of their perimeters is 16 cm , find the sides of two squares.

Answer 1

Let the square be of sides of length a and b.
then according to the question,

a²+ b²=400 (sum of areas)
_____________
4a-4b =16 (difference of perimeter)
a- b = 4
_________________
a²+ b²=400
(a-b)²+2ab= 400
2ab = 400 - 4² =384
__________________
(a+b)² = (a-b)² + 4ab= 4² + 2× 384
= 784
a + b =√784 = 28
__________________

a +b = 28
a - b = 4
+. +. +
2a = 32
a =16
b =12
hence,the square are of sides 16cm and 12 cm.