Question

If the hypotenuse of isosceles right triangle ABC is 8√2 what is the area of triangle ABC?

Answer 1

32 units squared, the third choice

Explanation:

1. Triangle ABC is a right isosceles one, meaning the relationships of the angles are 45:45:90.

2. The ratio of the sides for a 45:45:90 triangle is 1:1:
`√(2)`

3. The hypotenuse of ABC is
`8√(2)`, this means the other sides are 8 units long.

4. Area of a right triangle:
`(1)/(2)` * base * height.

5. Both the base and height are 8 units, so the formula should look like:

`(1)/(2) * 8 * 8 = 32`

6. The result is 32 units squared.

7. Triangle ABC's area is 32 units squared