Three sides of a triangle measure 3, 4, and 5. Solve for the length of the shortest side of a similar triangle whose longest side has a length of 20.(1 point) Responses 16 16 4 4 12 12 20

Answer 1

First, we identify the sides of the original triangle, which measures 3, 4, and 5. The longest side is 5.

We are tasked with finding the lengths of the sides of a similar triangle where the longest side measures 20. Since the triangles are similar, the sides are proportional.

To find the scale factor, we divide the corresponding sides of the triangles:

\[ \text{Scale Factor} = \frac{\text{Longest side of the new triangle}}{\text{Longest side of the original triangle}} = \frac{20}{5} = 4 \]

Now, we will multiply each side of the original triangle by the scale factor (4):

1. The shortest side (3): \[ 3 \times 4 = 12 \]

2. The next side (4): \[ 4 \times 4 = 16 \]

3. The longest side (5): \[ 5 \times 4 = 20 \]

Since we are looking for the length of the shortest side of the similar triangle, that is:

\[ \boxed{12} \]