The hypotenuse of a right isosceles triangle is $$18\sqrt3$$​ cm. Find the area of the triangle.

Correct option is A

Given:

The hypotenuse of a right isosceles triangle is 1$$8\sqrt{3}$$​ cm.
Formula Used:
In a right isosceles triangle, the two legs are equal in length, and the relationship between the legs and the hypotenuse follows the Pythagorean theorem:

​$$a^2 + a^2 = c^2$$​

where a is the length of each leg and c is the length of the hypotenuse.

The area of a right triangle is given by:

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

Solution:

From the Pythagorean theorem:

​$$a^2 + a^2 = (18\sqrt{3})^2$$​

​$$2a^2 = 18^2 \times 3$$​

​$$2a^2 = 324 \times 3 = 972$$​

​$$a^2 = \frac{972}{2} = 486$$​

​$$\text{Area} = \frac{1}{2} \times a^2 = \frac{1}{2} \times 486 = 243 \, \text{cm}^2$$​