Question

a wire of length 200 cm is cut into two parts and each part is bent to form a square.If the area of the larger square is 9 times that of the smaller square, find the perimeter of the larger square

Answer 1

The perimeter of the larger square is
`150cm.`

Explanation:

First of all, let one part of it be "
`x`"

and the other part of it "
`200-x`"

Now to solve this :

The area of the square =
`L^2`

The area of one part of the square =
`x^2`

The area of the other part of the square =
`(200-x)^2`

`9x^2= (200-x)^2\\9x^2=40000-400x+x^2`

Now, add,
`-4x^2` to both the sides :

`9x^2-9x^2=40000-400x+x^2-9x^2\\-1(8x^2+400x-40000)=0`

Now, take out the "8" which is common :

`-8(x^2+50x-5000)=0`

Now, divide it by
`-8` :

`x^2+100x-50x-5000=0\\x(x+100)-50(x+100)=0\\(x+100)(x-50)=0\\`

`x=-100` or
`50`

So, now we know that :

One of the part is =
`50cm`

And the other part is =
`150cm`

Thus the perimeter of the larger square is =
`150cm`