Question

Queen Parallela has 150 meters of fencing to build her pen for the dragon. Since she wants to make a rectangular pen, she knows that the area of the pen can be represented as A=ℓw, where ℓ=the length and w=the width. She also knows that the perimeter of a rectangle is P=2ℓ+2w.

Which expression would represent the length in terms of the width given that the width is x meters?


150−x

12(2x−150)

12(150−2x)

150+2x

Answer 1

Answer:
`(1)/(2)(150-2x)`

Explanation:

Given : Queen Parallela has 150 meters of fencing to build her pen for the dragon.

i.e. Perimeter of pen P = 150 meters

She also knows that the perimeter of a rectangle is P=2ℓ+2w, where ℓ=the length and w=the width.

if the width is x meters, then we have

`2l+2x=150`

Subtract 2x from both sides , we get

`2l=150-5x`

Divide both sides by 2, we get

`l=(1)/(2)(150-2x)`

Hence, the expression would represent the length in terms of the width :

`(1)/(2)(150-2x)`