Two triangles – one has base 15 cm and height 12 cm; find height of a second triangle with double the area and base 20 cm:

Introduction / Context:Relate triangle areas via A = (1/2) * base * height. If the second triangle has double the area of the first, scale accordingly.

Given Data / Assumptions:

• Triangle 1: base = 15 cm, height = 12 cm ⇒ A₁ = (1/2)*15*12 = 90 cm².
• Triangle 2: A₂ = 2*A₁ = 180 cm²; base₂ = 20 cm; height₂ = ?

Concept / Approach:height₂ = 2*A₂ / base₂ (rearranging A₂ = (1/2) * base₂ * height₂).

Step-by-Step Solution:

Verification / Alternative check:Check: (1/2)*20*18 = 180 cm², which is twice 90.

Why Other Options Are Wrong:16, 17, 20 do not satisfy the area condition with base 20 cm.

Common Pitfalls:Forgetting the 1/2 factor when solving for height.

Final Answer:18.