Math Problem Statement

Given right triangle A, B, CABC with altitude start overline, B, D, end overlineBD drawn to hypotenuse start overline, A, C, end overlineAC. If A, D, equals, 7AD=7 and B, D, equals, 14, commaBD=14, what is the length of start overline, D, C, end overline, question markDC?

Solution

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Math Problem Analysis

Mathematical Concepts

Geometry
Right Triangles
Proportionality in Similar Triangles

Formulas

AD * DC = BD^2 (geometric mean property of right triangles)
Sum of segment lengths: AC = AD + DC

Theorems

Geometric Mean Theorem
Similarity in Right Triangles

Suitable Grade Level

Grades 8-10