Question

Sum of the area of two squares is 400cm2.if the difference of their ,perimetres is 16 cm.find the sides of the two squares.

Answer 1

let sides of two squares are a and b

sum of their squares = 400cm2

a^2 + b^2 = 400 ------(1)

difference of their perimeters = 16cm

4a-4b = 16

divide each term with 4 we get

a-b = 4---(2)

square (2)

(a-b)^2 = 16

a^2+b^2 -2ab= 16

400-2ab =16

-2ab = 16-400

-2ab = -384

ab= -384/-2

ab= 192---(3)

find (a+b)^2

(a+b)^2=a^2+b^2+2ab
            =400+2*192
            =400+384

            =784
(a+b)^2 = (48)^2
a+b =48------(4)
subtract (2) from (4) we get
2a=52
a=52/2
a=26cm
substitute a=26 in (1)
26+b=48
b=48-26
b=22
sides of the two squares a= 26cm and b= 22cm