A parallelogram has a base that is twice its height. If the area of the parallelogram is 72 sq cm, find the height of the parallelogram in cm, keeping the “base is twice the height” condition unchanged.

Question

Solve this multiple-choice question and choose the correct option.

Accepted Answer

Introduction / Context:This is a basic mensuration question about the area of a parallelogram. The formula is area = base * height. Since the base is related to the height (base = 2 * height), you substitute this relationship into the area formula and solve a simple quadratic equation for the height. Given Data / Assumptions: Area of parallelogram = 72 sq cm Base b is twice the height h, so b = 2h Area formula: A = b * h Concept / Approach:Substitute b = 2h into A = b * h to get A = 2h^2. Solve for h using the given area value 72. Step-by-Step Solution: Step 1: A = b * h Step 2: Given b = 2h, so A = (2h) * h = 2h^2 Step 3: 2h^2 = 72 Step 4: h^2 = 72 / 2 = 36 Step 5: h = 6 cm (height is positive) Verification / Alternative check:If h = 6, then base b = 2 * 6 = 12. Area = 12 * 6 = 72 sq cm, exactly matching the given area. So the computed height is correct. Why Other Options Are Wrong: 7 cm: would give area = 2 * 7^2 = 98, not 72. 8 cm: would give area = 2 * 8^2 = 128, not 72. 9 cm: would give area = 2 * 9^2 = 162, not 72. 12 cm: would imply base 24 and area 288, far too large. Common Pitfalls:Students sometimes use the triangle area formula 1/2 * base * height by mistake. Another common error is taking h = 36 instead of sqrt(36). Always remember that h^2 = 36 implies h = 6, not 36. Final Answer:6 cm

A parallelogram has a base that is twice its height. If the area of the parallelogram is 72 sq cm, find the height of the parallelogram in cm, keeping the “base is twice the height” condition unchanged.

More Questions from Area

Discussion & Comments