Find the length of the hypotenuse of a larger triangle.

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.

Answer 1

First, we must determine the length of the hypotenuse of the smaller triangle. We can use the Pythagorean Theorem, which is a² + b² = c², where a and b are the legs of the triangle, and c is the hypotenuse.

 

3² + 4² = 9 + 16 = 25 = c²

 

5 = c

 

The smaller triangle has a hypotenuse of 5.

 

Since the scale factor is 1:3, can you now determine the length of the hypotenuse of the larger triangle, Alicen?

Answer 2

The hypotenuse of the smaller triangle is 5 (it is a 3-4-5 triangle)

The hypotenuse of the larger triangle is 15 (3 x 5)