A triangle has two equal sides of 13 cm each and third side of 10 cm. The area (in cm2) of the triangle is:

Correct option is A

Given:

Two equal sides = 13 cm each

Third side = 10 cm

Formula Used:
Semi-perimeter (s) of the triangle:

s$$= \frac{a + b + c}{2}$$​

where a, b, and c are the lengths of the sides.

The area A is then:

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

Solution:

Semi-perimeter s:

s $$= \frac{13 + 13 + 10}{2} = \frac{36}{2} = 18 \text{ cm}$$​

Area:

A =$$\sqrt{18 \times (18 - 13) \times (18 - 13) \times (18 - 10)}$$​

A $$= \sqrt{18 \times 5 \times 5 \times 8}$$​

​$$= \sqrt{18 \times 25 \times 8} = \sqrt{3600} = 60 \text{ cm}^2$$​

The area of the triangle is 60 cm².