The side lengths of a triangle are increased by 50% to make a similar triangle. Does the area increase by 50% as well? Explain.

The area of a triangle; A = a * h / 2 If we want to increase all sides by 50% we will have the sides of a similar triangle: a1 = 1.5 a, b1 = 1.5 b, c1 = 1.5 c. Also h1 = 1.5 h And the new area is: A1 = 1.5 a * 1.5 h / 2 = 2.25 a * h / 2 = 2.25 A Therefore the area is increased by 125%. Answer: **False. **

Answered by HomertheGenius | 2024-06-11

When the side lengths of a triangle are increased by 50%, the area does not increase by 50%. Instead, the area increases by 125%. This occurs because the area scales with the square of the linear dimensions, leading to an increase by a factor of 2.25.
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Answered by HomertheGenius | 2024-10-01