Question

A right isosceles triangle has side lengths of 13.2, 13.2, and 18.6 meters. What is the hypotenuse of a similar triangle with legs 4.4 meters in length

Answer 1

Answer: 6.2 meters

Reason

The jump from 4.4 to 13.2 is "times 3" because 13.2/4.4 = 3 which rearranges to 13.2 = 3*4.4

This would mean we triple each side of the smaller triangle to get the larger triangle. Take this in reverse to divide each side of the larger triangle by 3 to get the smaller triangle.

13.2/3 = 4.4

18.6/3 = 6.2

Answer 2

To find the hypotenuse of a similar triangle with legs of 4.4 meters each, you can set up a proportion using the ratios of corresponding sides of similar triangles.

In the original right isosceles triangle, the sides are in the ratio of 1:1:√2 because it's an isosceles right triangle, where the legs are congruent.

So, in the original triangle:

One leg = 13.2 meters

Another leg = 13.2 meters

Hypotenuse = 18.6 meters

The ratio of the legs to the hypotenuse in the original triangle is 1:1:√2.

Now, you want to find the hypotenuse of a similar triangle with legs of 4.4 meters each. Using the same ratio:

One leg = 4.4 meters

Another leg = 4.4 meters

Let "x" be the length of the hypotenuse in this similar triangle.

So, the ratio of the legs to the hypotenuse in the similar triangle is 1:1:x.

Now, you can set up a proportion:

1/1 = √2/x

Cross-multiply:

1 * x = 1 * √2

x = √2

Now, calculate the approximate value:

x ≈ 1.414

So, the hypotenuse of the similar triangle with legs of 4.4 meters each is approximately 1.414 meters.