Question

sum of the area of two squares is 468m^2 . If the difference of their perimeters is 24m find the side of the two square .​

Answer 1

Answer:

18m

12m

Step-by-step explanation:

Perimeter=side*4

Let side of smaller square be x,thus side of larger square is x+(24/4)=x+6

Area=s*s

Small area=x^2

Large area=(x+6)^2

Quadratic identity (a+b)^2=a^2+2ab+b^2

Large area=x^2+12x+36

Sum=x^2 + x^2+12x+36 = 2x^2+12x+36=468

Divide through by 2

x^2+6x+18=234

Arrange on one side

x^2+6x+18-234=0

x^2+6x-216=0

Factorise

Sum=6,product=-216

Factors=-12,18

x^2+18x-12x-234=0

x(x+18)-12(x+18)=0

(x-12)(x+18)=0

x=12 or-18

But it is not negative thus 12 is x

X-small side=12

X+6-large side=12+6=18

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