Competition problem — Geometry — Maths Olympiad Prep

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Geometry Difficulty 3.6 AMC 10/12 Find the answer United States

Problem:

Square $ABCD$ has side length $1$ . A dilation is performed about point $A$ , creating square $AB' C' D'$ . If $BC' = 29$ , determine the area of triangle $BDC'$ .

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

Solution:

$29^{2} - 2 \cdot \frac{1}{2}(29)\left(\frac{29}{2}\right) - \frac{1}{2} = 420$ .

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Source: MathNet, licensed CC-BY-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.