Question

the length of a rectangle is six times its width. if the perimeter of the rectangle is 84 ft, find its length and width. length: ft width: ft

Explanation:

Step1: Define variables

Let the width of the rectangle be \( w \) ft. Then the length \( l = 6w \) ft (since length is six times the width).

Step2: Recall perimeter formula

The perimeter \( P \) of a rectangle is given by \( P = 2(l + w) \). We know \( P = 84 \) ft. Substitute \( l = 6w \) into the formula:

$$ 84 = 2(6w + w) $$

Step3: Simplify and solve for \( w \)

Simplify the right - hand side: \( 2(6w + w)=2\times7w = 14w \). So we have the equation \( 14w=84 \). Divide both sides by 14: \( w=\frac{84}{14}=6 \) ft.

Step4: Find the length

Since \( l = 6w \), substitute \( w = 6 \) into this formula: \( l=6\times6 = 36 \) ft.

Answer:

length: \( 36 \) ft
width: \( 6 \) ft