Question

See the attachment, I don't know how to get the answer

Answer 1

`2x^(2) -5x-18 = 0`

x = 4.5 cm.

Explanation:

There are two rectangles in the compound shape ABCDEF.

The area of the small rectangle is x (x - 4) sq. cm.

Again the area of the large rectangle is (x - 2) (2x + x) = 3x (x - 2) sq. cm.

Therefore, the total are is x (x - 4) + 3x (x - 2) = 36 {Given}

⇒
`x^(2) -4x+3x^(2) -6x =36`

⇒
`4x^(2) -10x -36 =0`

⇒
`2x^(2) -5x-18 = 0` (Shown)

Now, solving this equation we get

`2x^(2) -9x+4x-18 = 0`

⇒
`(2x-9) (x+2) =0`

⇒ x = 4.5 and x = -2

Since x i.e. length of a side can not be negative. So, x = 4.5 cm. (Answer)