Question

Sun of the areas of two squares is 468m.if the difference of their perimeter is 24m find the sides of the two sides of the squares

Answer 1

If a square of side is 12 m then second other square side is 18 m

Answer 2

Let the length of smaller square be x

perimeter of smaller square =4x

Let the length of larger square be y

perimeter of larger square=4y

Now, 4x-4y=24m

or y-x=6 ( dividing both sides by 4)

or y=x+6

Now area of larger square=y×y=(x+6) +(x+6)

=x2+12x+36

Now area of smaller square. =x2

A/Q

x2+12x+36+x2=468

or x2 +6x+18=234(dividing both sides by 2)

or x2+6x+18-234=0

or x2 +6x-216=0

or (x+18) (x-12)=0 (on factoring the equation)

or x= -18,12

Since x cannot be negative , therefore

x=12

So the sides are 18m and 12m respectively.

Hope that helps.