The hypotenuse of a triangle was 8 cm and the hypotenuse of the final triangle was 72 cm. What is the scale factor?
To find the scale factor, we need to compare the lengths of corresponding sides of the original triangle and the final triangle.
Let x be the original length of one of the legs of the triangle. Using the Pythagorean theorem, we can find the other leg:
x^2 + x^2 = 8^2
2x^2 = 64
x^2 = 32
x = √32
x ≈ 5.65 cm
So, the original triangle had side lengths of approximately 5.65 cm, 5.65 cm, and 8 cm.
Now, let's find the scale factor by comparing the original triangle to the final triangle. The length of the hypotenuse in the final triangle is 72 cm, which is 9 times longer than the original length of 8 cm:
72 cm / 8 cm = 9
Therefore, the scale factor is 9:1.