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Quantitative Aptitude Question on Geometry

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

A circle of diameter 8 inches is inscribed in a triangle ABC where ∠ABC = 90°

Inradius =P+B−H2=\frac {P+B-H}{2}
4=P+10−H24=\frac {P+10-H}{2}
P+10−H=8P+10-H=8
P−H=−2P-H=-2
H=P+2H=P+2
Apply Pythagorus Theorem,
P2−(10)2=H2P^2-(10)^2=H^2
P2−100=(P+2)2P^2-100=(P+2)^2
P2−100=P2+4+4PP^2-100=P^2+4+4P
4P=964P=96
P=24P=24
Now, the area of the triangle,
=12×B×H=\frac 12 \times B \times H

=12×10×24=\frac 12 \times 10 \times 24
=120=120 square inches

So, the answer is 120120 square inches.