Question

a rectangle has a length of 15x and a width of 2x^3+4-2x^2. Find the perimeter of the rectangle when the length is 5 feet

Answer 1

The perimeter of the rectangle is 17.70 feet

Explanation:

- The perimeter of a rectangle is → P = 2l + 2w → where l is its length

and w is its width

- A rectangle has a length 15x and a width 2x³ + 4 - 2x²

- We need to find its perimeter when its length is 5 feet

∵ The length of the rectangle is 15x

∵ The length of the rectangle is 5 feet

- Equate the length's expressions

∴ 15x = 5

- Divide both sides by 15

∴
`x=(1)/(3)`

- Now lets find the width of the rectangle

∵ The width of the rectangle = 2x³ + 4 - 2x²

∵
`x=(1)/(3)`

- Substitute the value of x in the expression of the width

∴
`w=2((1)/(3))^(3)+4-2((1)/(3))^(2)`

∴
`w=2((1)/(27))+4-2((1)/(9))`

∴
`w=(2)/(27)+4-(2)/(9))`

∴
`w=(104)/(27)` feet

∵ l = 5 feet and
`w=(104)/(27)` feet

∵ P = 2l + 2w

∴ P = 2(5) +
`2((104)/(27))`

∴ P = 10 +
`(208)/(27)`

∴ P = 17.70 feet

* The perimeter of the rectangle is 17.70 feet