Question

Consider the points (a, a), (-a, -a), and (-3a, 3a) forming a triangle. If the triangle is right-angled at A and is equilateral, what is its area?

a. 3√3a²/2
b. 2√3a²/3
c. √3a²/2
d. √3a²/4

Answer 1

The area of the equilateral right-angled triangle can be found using the Pythagorean theorem and the formula for the area of an equilateral triangle.

Step-by-step explanation:

To find the area of the triangle, we can use the fact that the triangle is equilateral. An equilateral triangle has all three sides and angles equal. Since the triangle is also right-angled at point A, we can use the Pythagorean theorem to find the length of the sides.

The Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse.

In this case, the hypotenuse of the right triangle is the side of the equilateral triangle, which is 2a.

So we have (2a)² = a² + a², which simplifies to 4a² = 2a². Dividing both sides by 2 gives us 2a² = a².

Now, we can find the area of the equilateral triangle using the formula A = (√3/4) * side².

Substituting the side length with 2a, we have A = (√3/4) * (2a)² = (√3/4) * 4a² = √3a²/2.