A triangle has base 15 cm and height 12 cm. Another triangle has double the area of the first triangle and has base 20 cm. Find the height (in cm) of the second triangle.

Introduction / Context:
This question tests the triangle area formula and proportional reasoning. The area of a triangle is (1/2)*base*height. First compute the area of the original triangle, then double it. For the second triangle, the base is known, so you rearrange the same formula to solve for height. The core skill is using the same area relationship with correct arithmetic and units.

Given Data / Assumptions:

• Triangle 1: base b1 = 15 cm, height h1 = 12 cm
• Triangle 2: base b2 = 20 cm
• Area of triangle 2 = 2*(area of triangle 1)

Concept / Approach:
Compute area1 = (1/2)*b1*h1. Then area2 = 2*area1. Finally, use area2 = (1/2)*b2*h2 and solve for h2: h2 = (2*area2)/b2.

Step-by-Step Solution:
Area1 = (1/2)*15*12 = (1/2)*180 = 90 sq cmArea2 = 2*Area1 = 2*90 = 180 sq cmArea2 = (1/2)*20*h2 = 10*h210*h2 = 180 => h2 = 18 cm

Verification / Alternative check:
Check: With base 20 and height 18, area = (1/2)*20*18 = 180 sq cm, which is exactly double 90 sq cm. So the computed height is correct.

Why Other Options Are Wrong:
16 and 17 come from arithmetic slips (often doubling the base instead of area). 20 occurs if you forget the 1/2 in the formula. 15 results from mistakenly keeping the same height as the first triangle without respecting the “double area” condition.

Common Pitfalls:
Forgetting the 1/2 factor. Doubling the base instead of doubling area. Mixing up which triangle has which base. Doing 180/20 instead of (2*180)/20 when rearranging the formula.

Final Answer:
18 cm