Questions: Finding the perimeter or area of a rectangle given one of these values The length of a rectangle is 3 in longer than its width. If the perimeter of the rectangle is 26 in, find its area.

Solution Steps

To solve this problem, we need to use the relationship between the length and width of the rectangle and the formula for the perimeter. We can set up equations based on the given information and solve for the width and length. Once we have these dimensions, we can calculate the area.

1. Let the width of the rectangle be \( w \).
2. The length of the rectangle is \( w + 3 \).
3. The perimeter of the rectangle is given by \( 2 \times (\text{length} + \text{width}) = 26 \).
4. Solve for \( w \) and then find the length.
5. Calculate the area using the formula \( \text{length} \times \text{width} \).

Let the width of the rectangle be \( w \). According to the problem, the length \( l \) can be expressed as: \[ l = w + 3 \]

The formula for the perimeter \( P \) of a rectangle is given by: \[ P = 2(l + w) \] Substituting the known perimeter: \[ 2((w + 3) + w) = 26 \]

Expanding the equation: \[ 2(2w + 3) = 26 \] Dividing both sides by 2: \[ 2w + 3 = 13 \] Subtracting 3 from both sides: \[ 2w = 10 \] Dividing by 2: \[ w = 5 \]

Using the width to find the length: \[ l = w + 3 = 5 + 3 = 8 \]

The area \( A \) of the rectangle is given by: \[ A = l \times w = 8 \times 5 = 40 \]

Final Answer