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

Answer:

The perimeter of the rectangle is 17.70 feet

Step-by-step 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

∴ $x=\frac{1}{3}$

- Now lets find the width of the rectangle

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

∵ $x=\frac{1}{3}$

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

∴ $w=2(\frac{1}{3})^{3}+4-2(\frac{1}{3})^{2}$

∴ $w=2(\frac{1}{27})+4-2(\frac{1}{9})$

∴ $w=\frac{2}{27}+4-\frac{2}{9})$

∴ $w=\frac{104}{27}$ feet

∵ l = 5 feet and $w=\frac{104}{27}$ feet

∵ P = 2l + 2w

∴ P = 2(5) + $2(\frac{104}{27})$

∴ P = 10 + $\frac{208}{27}$

∴ P = 17.70 feet

* The perimeter of the rectangle is 17.70 feet