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
∴ [tex]x=\frac{1}{3}[/tex]
- Now lets find the width of the rectangle
∵ The width of the rectangle = 2x³ + 4 - 2x²
∵ [tex]x=\frac{1}{3}[/tex]
- Substitute the value of x in the expression of the width
∴ [tex]w=2(\frac{1}{3})^{3}+4-2(\frac{1}{3})^{2}[/tex]
∴ [tex]w=2(\frac{1}{27})+4-2(\frac{1}{9})[/tex]
∴ [tex]w=\frac{2}{27}+4-\frac{2}{9})[/tex]
∴ [tex]w=\frac{104}{27}[/tex] feet
∵ l = 5 feet and [tex]w=\frac{104}{27}[/tex] feet
∵ P = 2l + 2w
∴ P = 2(5) + [tex]2(\frac{104}{27})[/tex]
∴ P = 10 + [tex]\frac{208}{27}[/tex]
∴ P = 17.70 feet
* The perimeter of the rectangle is 17.70 feet
