Question

question
the right triangle on the right is a scaled copy of the right triangle on the left. identify the scale factor. express your answer as a whole number or fraction in simplest form.
3
4
9/2
6

Explanation:

Step1: Recall scale factor formula

The scale factor is the ratio of a corresponding side length in the scaled copy (right triangle) to the corresponding side length in the original (left triangle). Let's take the vertical sides: original length is \( 3 \), scaled length is \( \frac{9}{2} \). Or take horizontal sides: original is \( 4 \), scaled is \( 6 \). We can use either pair. Let's use vertical sides first.

Step2: Calculate scale factor

Scale factor \( = \frac{\text{Scaled length}}{\text{Original length}} \). Using vertical sides: \( \frac{\frac{9}{2}}{3} = \frac{9}{2} \times \frac{1}{3} = \frac{3}{2} \). Let's check with horizontal sides: \( \frac{6}{4} = \frac{3}{2} \). Both give the same result.

Answer:

\(\frac{3}{2}\)