Right-angled triangle — The area is 40 sq cm. If the base is 28 cm, find the corresponding height (use area = 1/2 * base * height).

Introduction / Context:This is a direct application of the right-triangle area relation. Knowing area and one leg (the base), we can back-compute the other leg (the height) without using Pythagoras because no hypotenuse is involved.

Given Data / Assumptions:

• Area = 40 sq cm
• Base = 28 cm
• Right-angled triangle: area formula holds as 1/2 * base * height

Concept / Approach:Area of a right triangle equals 1/2 * base * height. Rearranging gives height = (2 * Area) / base. Substitute the given values to get an exact fractional height.

Step-by-Step Solution:height = (2 * 40) / 28height = 80 / 28 = 20 / 7 cmThus the required height is 20/7 cm ≈ 2.857 cm

Verification / Alternative check:Check by plugging back: area = 1/2 * 28 * (20/7) = 14 * (20/7) = 40 ✔

Why Other Options Are Wrong:26/7, 36/7, 46/7, 56/7 give areas other than 40 when used in 1/2 * 28 * height; they are distractors based on arithmetic slips.

Common Pitfalls:Forgetting the factor 1/2 in the area formula or attempting to use Pythagoras when only area and one leg are needed.

Final Answer:20/7 cm