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?
Answer & explanation
Correct answer: option 2
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