Question

HELPPP PLZZZ

A square tabletop has an area of (9x^2-90x+225) cm^2. The dimensions of the tabletop have the form cx-d, where c and d are whole numbers. Write an expression for the perimeter of the tabletop. Then find the perimeter when x=25 centimeters.

Answer 1

Explanation:

Given: A square tabletop has an area of
`(9x^2-90x+225)cm^2`.The dimensions of the tabletop have the form cx-d, where c and d are whole numbers.

To find: Expression for the perimeter of the tabletop and the perimeter when x=25 centimeters.

solution: Since, we know that area of square =
`(side)^2`, and we are given Area=
`(side)^(2)`=
`9x^2-90x+225`

⇒
`s^(2)=(3x-15)(3x-15)`

⇒
`s^2=(3x-15)^2`

⇒
`s=3x-15`

Thus, side=
`3x-15`.

Now, Perimeter of square is given as =4s

⇒
`4s=4(3x-15)=12x-60` which is the required expression for the perimeter.

Perimeter when x=25cm,
`12x-60=12(25)-60=300-60=240cm`.

Therefore, Perimeter=240 cm.