Question

The hypotenuse of an isosceles right triangle is $14\sqrt 2$. What is the area of the triangle?

Answer 1

The area of the triangle is 98 square units.

If it is an isosceles right triangle, then it is also a 45 45 90 triangle. Therefore, we can use the ratios of this special triangle to know that the two legs are 14.

Now just find the area:

14 x 14 / 2 = 98

Answer 2

The area is 98.

In an isosceles right triangle, the lengths of the sides are given by t, t and t√2. The longest side, the hypotenuse, is represented by t√2 and the legs are both given by t.

We know that the hypotenuse is 14√2:
t√2 = 14√2

This means t=14.

To find the area of triangle, we use the formula A=1/2bh:
A=1/2(7)(7) = 98