Question

A circle of diameter 8 inches is inscribed in a triangle ABC where ∠ABC = 90°. If BC = 10 inches then the area of the triangle in square inches is

Answer 1

Inradius \(=\frac {P+B-H}{2}\)
\(4=\frac {P+10-H}{2}\)
\(P+10-H=8\)
\(P-H=-2\)
\(H=P+2\)
Apply Pythagorus Theorem,
\(P^2-(10)^2=H^2\)
\(P^2-100=(P+2)^2\)
\(P^2-100=P^2+4+4P\)
\(4P=96\)
\(P=24\)
Now, the area of the triangle,
\(=\frac 12  \times B \times H\)

\(=\frac 12  \times 10 \times 24\)
\(=120\) square inches

So, the answer is \(120\) square inches.