Question

Find the area of an equilateral triangle whose area is equal to the triangle of sides 12 cm, 8 cm and 16 cm.

• A. 12√15 cm²
• B. 15√15 cm²
• C. 18√15 cm²
• D. 20√15 cm²

Answer 1

The correct option is A

12√15 cm²

We can get the area of another triangle by using Heron’s formula

a = 12 cm, b = 8 cm and c = 16 cm

s =$\frac{a+b+c}{2}$ = 18 cm

Area = $\sqrt{s(s-a)(s-b)(s-c)}$

$=\sqrt{18(18-12)(18-8)(18-16)}$

$=\sqrt{18\times 6\times 10\times 2}$

$=12\sqrt{15}c{m}^2$