Chapter E, Problem 11.16EX

To determine

To find the area of the triangle with sides 15, 15 and 24.

Answer to Problem 11.16EX

Option (d)

Explanation of Solution

Given information: Triangle with sides 15, 15 and 24.

Concept used:

  $\begin{array}{l}\text{Area of the triangle}\text{=}\sqrt{s(s-a)(s-b)(s-c)}\\ \text{where,}s=\frac{a+b+c}{2};a,b\text{and}c\text{are}\text{the}\text{sides}\text{of}\text{the}\text{}\text{triangle}\text{.}\\ \text{Perimeter of the equilateral triangle}=3a\end{array}$

Here, a = 15, b = 15, c = 24

  $\begin{array}{l}s=\frac{15+15+24}{2}=27\\ \text{Area of the triangle}\text{=}\sqrt{27(27-15)(27-15)(27-24)}\\ =\sqrt{27(12)(12)(3)}=108\end{array}$

Hence, the area of the triangle is 108 square units.