Question

In a triangle ABC, 2 sides AB and AC are of length 5 units each. If a perpendicular of length 3 units is dropped from A to BC, then what is the length of the radius of the circle that can be inscribed in the triangle?

• A. 3
• B. 1.33
• C. 2
• D. 2.5

Answer 1

The correct option is B 1.33

option (b)

3 sides of the triangle along with the perpendicular forms 2 right-angled triangles.
The3${}^{rd}$ side(base of triangle) is hence $\sqrt{(5^2-3^2)}+\sqrt{(5^2-3^2)}$ = 8.

Area of the triangle = $\frac{1}{2}$$\times$3$\times$8 = rs = $\frac{(a+b+c)r}{2}$, where s is the semi-perimeter and r is the in-radius of the triangle.
Solving r = $\frac{24}{18}$ = 1.33