freyesinsb wrote:Looking for various approaches to this Algebra problem disguised as a Geometry question.
In right triangle ABC, BC is the hypotenuse. If BC is 13 and AB + AC = 15, what is the area of the triangle?
A. 2√7
B. 2√14
C. 14
D. 28
E. 56
Source: Veritas Prep
OA: C
(AB + AC)² = 15²
AB² + 2(AB)(AC) + AC² = 225.
AB² + AC² + 2(AB)(AC) = 225.
Since ∆ABC is a right triangle:
AB² + AC² = BC²
AB² + AC² = 13²
AB² + AC² = 169.
Substituting AB² + AC² = 169 into AB² + AC² + 2(AB)(AC) = 225, we get:
169 + 2(AB)(AC) = 225
(AB)(AC) = 28.
Since A = (1/2)(AB)(AC), we get:
A = (1/2)(28) = 14.
The correct answer is
C.
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