Question

Two right triangles are similar. The legs of the smaller triangle have lengths of 3 and 4. The scale factor is 1:3. Find the length of the hypotenuse of the larger triangle. The length of the hypotenuse of the larger triangle is

Answer 1

Answer:

15 units.

Step-by-step explanation:

The hypotenuse of the smaller triangle = sqrt (3^2 + 4^2)

= sqrt 25 = 5.

As the scale factor is 1:3 the hypotenuse of the larger triangle = 5 * 3

= 15.

Answer 2

The length of the hypotenuse of the larger triangle is 15.

How to find the length of the hypotenuse of the larger triangle?

Using the smaller triangle, we find its hypotenuse,

using Pythagorean Theorem:

${data-answer}amp;h^{2}=3^{2}+4^{2}$

${data-answer}amp;h^{2}=9+16$

$&h^{2}=25$

$&h=\sqrt{25}$

h = 5

Let x be the hypotenuse of the larger triangle.

Using the scale factor, we can write the proportion as

${data-answer}amp;\frac{1}{3}=\frac{h}{x}$

${data-answer}amp;\frac{1}{3}=\frac{5}{x}$

x = 3(5)

x = 15

Therefore, the length of the hypotenuse of the larger triangle is 15.

To learn more about Pythagorean Theorem

https://brainly.com/question/343682

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