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 12 12 20 20 4 4 16

Answer 1

The sides of the original triangle are 3, 4, and 5. The longest side of this triangle is 5.

To find the scale factor for the similar triangle, we compare the longest side of the new triangle (20) with the longest side of the original triangle (5):

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

Now, we can find the lengths of the other sides of the similar triangle by multiplying each side of the original triangle by the scale factor:

For the side that measures 3: \[ 3 \times 4 = 12. \]

For the side that measures 4: \[ 4 \times 4 = 16. \]

For the side that measures 5: \[ 5 \times 4 = 20. \]

Thus, the lengths of the sides of the similar triangle are 12, 16, and 20.

The shortest side of the similar triangle is therefore: \[ \boxed{12}. \]