The length of a rectangle is 10 cm. If its perimeter is 28 cm, find the area

Analyze the question: We are given the length of a rectangle (10 cm) and its perimeter (28 cm). We need to find the width first, then the area.

Concept:

• Perimeter of a rectangle: P = 2(l + w)
• Area of a rectangle: A = l × w

Solution:

Step 1: Substitute into the perimeter formula. 28 = 2(10 + w)

Step 2: Divide both sides by 2. 14 = 10 + w

Step 3: Solve for w. w = 14 − 10 = 4 cm

Step 4: Find the area. A = l × w = 10 × 4 = 40 cm²

Check: Perimeter = 2(10 + 4) = 2(14) = 28 cm ✓

Answer: The area is 40 cm², which is option B.

Tip: For perimeter problems, always halve the perimeter first. Here, l + w = 28 ÷ 2 = 14, so w = 14 − 10 = 4. This saves time in the exam. Don't mix up perimeter (the distance around the shape) with area (the space inside it).