Question

In an isosceles right triangle with a hypotenuse of x√6 units, what is the area of the triangle?

Answer 1

In an isosceles right triangle with a hypotenuse of x√6 units, the area of the triangle is (3x^2) / 2.

Step-by-step explanation:

In an isosceles right triangle, two sides are congruent in length. Let's denote one of the legs as a and the hypotenuse as x√6. Since the triangle is right, we can use the Pythagorean theorem to find the length of the other leg:

a2 + a2 = (x√6)2

Simplifying, we get: 2a2 = 6x2

a2 = 3x2

Now, to find the area of the triangle, we can use the formula for the area of a triangle: Area = (base * height) / 2. Since the triangle is isosceles, the base and height are the same, so we can use a for both:

Area = (a * a) / 2 = a2 / 2

Substituting the value of a from above, we get: Area = (3x2) / 2