Question

the length of a rectangle is 3 m longer than its width. if the perimeter of the rectangle is 26 m, find its area.

Explanation:

Step1: Define variables

Let the width of the rectangle be \( w \) meters. Then the length \( l = w + 3 \) meters.

Step2: Use perimeter formula

The perimeter of a rectangle is given by \( P = 2(l + w) \). We know \( P = 26 \), so substitute \( l = w + 3 \) into the formula:

$$ 2((w + 3) + w) = 26 $$

Simplify inside the parentheses:

$$ 2(2w + 3) = 26 $$

Divide both sides by 2:

$$ 2w + 3 = 13 $$

Subtract 3 from both sides:

$$ 2w = 10 $$

Divide by 2:

$$ w = 5 $$

Step3: Find length

Now find the length: \( l = w + 3 = 5 + 3 = 8 \) meters.

Step4: Calculate area

The area of a rectangle is \( A = l \times w \). Substitute \( l = 8 \) and \( w = 5 \):

$$ A = 8 \times 5 = 40 $$

Answer:

\( 40 \)