Question

the length of a rectangle is four times its width. if the perimeter of the rectangle is 70 yd, find its length and width. length: \\(\square\\) yd width: \\(\square\\) yd

Explanation:

Step1: Define variables

Let the width of the rectangle be \( w \) yd. Then the length \( l \) is \( 4w \) yd (since length is four times the width).

Step2: Use perimeter formula

The perimeter \( P \) of a rectangle is given by \( P = 2(l + w) \). We know \( P = 70 \) yd. Substitute \( l = 4w \) into the formula:

$$ 70 = 2(4w + w) $$

Step3: Simplify and solve for \( w \)

Simplify the right - hand side: \( 2(4w + w)=2(5w) = 10w \). So we have the equation \( 10w=70 \). Divide both sides by 10: \( w=\frac{70}{10}=7 \) yd.

Step4: Find the length

Since \( l = 4w \), substitute \( w = 7 \) into this formula: \( l=4\times7 = 28 \) yd.

Answer:

length: \( 28 \) yd
width: \( 7 \) yd