Question

If the lengths of a sides of a triangle are in the ratio 4 : 5 : 6 and the in-radius of the triangle is 3 cm, then the altitude of the triangle corresponding to the largest side as the base is: 

(a) 8 cm 

(b) 7.5 cm 

(c) 6 cm 

(d) 10 cm

Answer 1

(b) 7.5 cm.

Area of a triangle = \(\frac{1}{2}\)x base x height

= In-radius x semi-perimeter of the Δ \(\big[\text{Using r =}\frac{\Delta}{s}\big]\)

Let the sides of triangle be 4x, 5x and 6x respectively. 

Given: In-radius = 3 cm

Therefore, 3 x \(\frac{(4x+5x+6x)}{2}\) = \(\frac{1}{2}\) x 6\(x\) x h, where h is the height.

⇒ 3 x \(\frac{15x}{2}\) = \(\frac{6x}{2}\) x h ⇒ h = \(\frac{45}{6}\) = 7.5 cm.