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Joe wants to build a doll house that looks just like his house. The house is 30 feet wide and 35 feet tall at the roof's highest point. If the doll house is to be 2.5 feet wide, about how tall should its highest point be?
AAbout 2.9 feet
BAbout 3.5 feet
CAbout 2.5 feet
DAbout 4.2 feet
Answer & Solution
Correct answer: A. About 2.9 feet
1. A scale model keeps corresponding measurements in the same ratio, like similar triangles.
2. Set up the proportion: house width over doll house width equals house height over doll house height, so 30 over 2.5 equals 35 over h.
3. Cross multiply: 30h equals 2.5 times 35, which is 87.5.
4. Divide by 30: h equals 87.5 divided by 30, which is about 2.9 feet.
5. Reusing the width and making it about 2.5 feet tall would squash the roof, since the real house is taller than it is wide.
_Source: OpenStax Prealgebra (CC BY 4.0), Ch 9 "Math Models and Geometry", section 9.3 Use Properties of Angles, Triangles, and the Pythagorean Theorem_
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