The hypotenuse of a right isosceles triangle is $$34\sqrt2$$​ cm. Find the area of the triangle.

Correct option is D

Given:

The hypotenuse of a right isosceles triangle =$$34\sqrt2$$​ cm

Concept Used:

In a right isosceles triangle, the two sides are of equal length. Let, height = base = a, hypotenuse= h.

By the Pythagorean theorem:

​$$h = a\sqrt{2}$$​

The area of the triangle is given by:

​$$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$$​​

Solution:

​$$34\sqrt{2} = a\sqrt{2}$$​

a = 34 cm

Area =$$\frac1{2} \times 34 \times 34 = \frac{1156}{2} = 578 \, \text{cm}^2$$​

Thus, the area of the triangle is 578 cm².