Question

the length of a rectangle is twice its width. if the perimeter of the rectangle is 36 m, find its length and width. length: □ m width: □ m

Explanation:

Step1: Define variables

Let the width of the rectangle be \( w \) meters. Then the length \( l \) is \( 2w \) meters (since length is twice the width).

Step2: Recall perimeter formula

The perimeter \( P \) of a rectangle is given by \( P = 2(l + w) \). We know \( P = 36 \) m. Substitute \( l = 2w \) into the formula:
\[
36 = 2(2w + w)
\]

Step3: Simplify and solve for \( w \)

Simplify the expression inside the parentheses: \( 2w + w = 3w \). So the equation becomes:
\[
36 = 2(3w) = 6w
\]
Divide both sides by 6:
\[
w = \frac{36}{6} = 6
\]

Step4: Find the length

Since \( l = 2w \), substitute \( w = 6 \):
\[
l = 2 \times 6 = 12
\]

Answer:

length: \( 12 \) m
width: \( 6 \) m