If in triangle, angles are in the ratio 1 : 1 : 2 and the length of its longest side is $6\sqrt{2}$cm, then what is the Area (in cm²) of the triangle?

18

We have,

Angles of triangle are in the ratio = 1 : 1 : 2

The length of its longest side = 6\(\sqrt {2}\) cm

Let the angles are a, a and 2a

We know the sum of angles of triangle = 180°

= a + a + 2a = 180°

= 4a = 180°

= a = 45°

The angles of triangle are 45°, 45° and 90°

The triangle is an isosceles triangle, If we take the equal side of isosceles triangle ‘s’

Then its longest side will be \(\sqrt {2}\)s

So, \(\sqrt {2}\)s = 6\(\sqrt {2}\) cm

= s = 6

The equal sides are of 6 cm

Area of triangle = \(\frac{1}{2}\) × 6 × 6

The area of the triangle = 18 cm²