Question

the perimeter of a rectangle is 45 m. its length is 5 m longer than its width. what is the width and length? draw it here.

Explanation:

Step1: Define variables

Let the width of the rectangle be \( w \) meters. Then the length \( l \) is \( w + 5 \) meters (since length is 5 m longer than width).

Step2: Use perimeter formula

The perimeter \( P \) of a rectangle is given by \( P = 2(l + w) \). We know \( P = 45 \) m. Substitute \( l = w + 5 \) into the formula:
\[
45 = 2((w + 5) + w)
\]

Step3: Simplify the equation

First, simplify the expression inside the parentheses:
\[
45 = 2(2w + 5)
\]
Then distribute the 2:
\[
45 = 4w + 10
\]

Step4: Solve for \( w \)

Subtract 10 from both sides:
\[
45 - 10 = 4w
\]
\[
35 = 4w
\]
Divide both sides by 4:
\[
w=\frac{35}{4}=8.75
\]

Step5: Find the length

Now that we have the width, find the length using \( l = w + 5 \):
\[
l = 8.75 + 5 = 13.75
\]

Answer:

The width of the rectangle is \( 8.75 \) m and the length is \( 13.75 \) m.