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

1 answer

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:

\[ \boxed{12} \]