NDA 2016 Maths · Mathematics · Properties of Triangles · medium

The area of a triangle whose sides are 4, 5 and 6 is

Single correct option

The area of a triangle whose sides are

4

5

and

6

Show answer and solution

Answer: (A) $\dfrac{15\sqrt7}4$

The semi-perimeter is

s=\dfrac{15}2

. Heron's formula gives

\Delta=\sqrt{\dfrac{15}2\cdot\dfrac72\cdot\dfrac52\cdot\dfrac32}=\sqrt{\dfrac{1575}{16}}=\dfrac{15\sqrt7}4

. Using the full perimeter

15

in place of

s

would give a much larger area.

Original question written in the NDA 2016 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake