Find the area of the isosceles triangle with a hypotenuse of length 10 ft.

Question

Find the area of the isosceles triangle with a hypotenuse of length 10 ft.

Answer 1

An isosceles right triangle is a right triangle with two congruent legs and acute angles. Because the legs are the same length, the ratio of a leg to the hypotenuse can be defined as 1:√2. So if we were to represent the length of each side using x, then each leg would be x and the hypotenuse would be (√2)x. Using this ratio, we can find the length of each of the sides.

hypotenuse =

(√2)x = 10

x = 10 / √2

= 10 √2 / (√2 * √2)

= 10 √2 / 2

= 5 √2

So each leg of the triangle has a length of 5 √2 ft. I haven't rationalized yet because radicals are easier to work with that decimals in this case.

Area of a triangle can be defined as A = (H * B) / 2, where H is the height of the triangle, and B is the base. In this case, the height and base are the legs, which are both the same height. Substitute your values into the formula:

A = (H * B) / 2

= (5 √2) (5 √2) / 2

= (25 * 2) / 2

= 50 / 2

= 25 ft²

Answer 2

Hi! So if the triangle has a hypotenuse and is isosceles, we're working with a special right triangle - specifically, a 45°-45°-90°. That means that the two legs are the same length, and the hypotenuse is the length of a leg times √2. In the case of this triangle, if we do 10 ÷ √2, you get 5√2 for the length of a leg.

So now, when you use the formula for area of a triangle, which is (bh)/2, that's gonna be (5√2) (5√2) = 50ft².

Hope this helps. :)

Answer 3

So you've got two answers (I don't mean to criticize tutors; everyone makes mistakes). I posed the question to ChatGPT and got a third answer. But now what do you do?

Take charge! First, make sure you know what the words hypotenuse and isosceles mean. Then, draw a triangle and label it. next, apply the pythagorean theorem and the area of a triangle to solve the problem. Finally, come back here and with confidence tell us which answer is correct.

So what good are tutors you might ask? My answer is this: tutors are here to guide you to find the answers yourself, not to simply provide answers.