In a triangle, ABC, AB = AC and the perimeter of △ABC is 8(2 +√2) cm. If the length of BC is √2 times the length of AB, then find the area of △ABC.
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 32 cm2
Let AB = x cm, then
AB = AC = x and BC = √2x.
Ratio of the sides of the triangle = x : x : √2x
= 1 : 1 : √2
Now one can directly say that it is a 45 : 45 : 90 triangle.
Perimeter = x + x + √2x = 8(2 +√2)
x + x + x = 8 + 8 + 8√2
x = 8.
Area of triangle ABC = 1/2 × 8 × 8 = 32 cm2.