Question

A right isosceles triangle has side lengths of 13.2, 13.2, and 18.6 meters. what is the hypotenuse Are there similar triangle with legs 4.4 meters in length?

Answer 1

In a right isosceles triangle, the two legs are equal in length. Therefore, if the side lengths are 13.2 meters and 13.2 meters, then the hypotenuse (the third side) can be found using the Pythagorean theorem.

Let's denote the hypotenuse as x. According to the Pythagorean theorem, we have:

(13.2)^2 + (13.2)^2 = x^2
174.24 + 174.24 = x^2
348.48 = x^2

Taking the square root of both sides, we find:

x = √348.48
x ≈ 18.66 meters

So, the hypotenuse of the right isosceles triangle is approximately 18.66 meters.

Now, let's consider a similar triangle with legs of 4.4 meters in length. In similar triangles, the corresponding sides are proportional. Therefore, if we have a similar right isosceles triangle, the ratio of the lengths of corresponding sides will be the same.

Let's denote the hypotenuse of this similar triangle as y. Since the ratio of the sides should be the same, we can set up the following proportion:

13.2 / 18.6 = 4.4 / y

Cross-multiplying, we get:

13.2y = 4.4 * 18.6
13.2y = 81.84
y = 81.84 / 13.2
y ≈ 6.2 meters

So, if the legs of the right isosceles triangle are 4.4 meters, then the length of the hypotenuse of the similar triangle is approximately 6.2 meters.