Question

One of the sides of a triangle is divided into segments of 6 and 8 units by the point of tangency of the inscribed circle. If the radius of the circle is 4, then the length of the shortest side of the triangle is :

• A. 12 units
• B. 13 units
• C. 14 units
• D. 15 units
• E. 16 units

Answer 1

The correct option is B 13 units

BC = 14 units

$s=\frac{a+b+c}{2}s=m+14Area=\sqrt{s(s-a)(s-b)(s-c)}=\sqrt{(m+14)\left(m\right)\left(8\right)\left(6\right)}⟹\frac{1}{2}\left(4\right)\left(14\right)+\frac{1}{2}\left(4\right)(m+6)+\frac{1}{2}\left(4\right)(m+8)=Area⟹4(m+14)=\sqrt{(m+14)\left(m\right)\left(48\right)}⟹4\sqrt{m+14}=\sqrt{48m}⟹16(m+14)=48m⟹m+14=3m\therefore m=7$

$\therefore$ Length of the sides are = 13, 14, 15

$\therefore$ Shortest side of the triangle = 13 units