This is a data sufficiency question about a right-angled triangle. Question: What is the height (perpendicular) of the right-angled triangle? Statement A: The area of the triangle is 20 times its base. Statement B: The perimeter of the triangle is equal to the perimeter of a square having side 10 cm. Decide which statement(s) is/are sufficient to determine the height uniquely (without needing any additional information).

Introduction / Context:Data sufficiency questions test whether given statements provide enough information to answer a question, not whether you can compute many values. Here, you must decide if the height of a right-angled triangle can be uniquely determined. The right-triangle area formula involves base and height directly, while the perimeter statement relates to side lengths but may not uniquely fix the height without additional relationships.

Given Data / Assumptions:

• We need the triangle’s height (perpendicular to the base)
• Right-angled triangle area formula: area = (1/2) * base * height
• Statement A: area is 20 times the base
• Statement B: triangle perimeter equals perimeter of a square of side 10 cm (so perimeter = 40 cm)

Concept / Approach:Check each statement independently. A is sufficient if it directly yields height. B is sufficient only if perimeter alone uniquely determines height, which generally it does not for right triangles unless more constraints are provided.

Step-by-Step Solution:

Verification / Alternative check:Statement A gives a single value height = 40 cm regardless of base, so it uniquely determines the height and is sufficient alone. Statement B gives only a perimeter total, which can correspond to multiple sets of sides (and thus multiple heights), so it is insufficient alone.

Why Other Options Are Wrong:

Common Pitfalls:Many learners confuse data sufficiency with “can I compute something.” You must check uniqueness. Another mistake is forgetting that base cancels in statement A, making height independent of base value. For statement B, assuming a unique triangle from perimeter alone is incorrect.

Final Answer:Only statement A is sufficient