Triangle D has been dilated to create triangle D′. Use the image to answer the question.

Question

image of a triangle labeled D with side lengths of 2.7, 4.8, 4.2 and a second triangle labeled D prime with side lengths of x, 1.6, 1.4

Determine the scale factor used.
2
3
one third
one half

Answer 1

To determine the scale factor between triangle D and triangle D', we can compare the corresponding side lengths of the two triangles.

The side lengths of triangle D are:

• 2.7
• 4.8
• 4.2

The corresponding side lengths of triangle D' are:

• x (unknown)
• 1.6
• 1.4

To find the scale factor, we will choose a corresponding pair of side lengths. Let's use the side of length 4.8 from triangle D and the side of length 1.6 from triangle D'.

The scale factor can be calculated as follows:

\[ \text{Scale factor} = \frac{\text{Length of triangle D'}}{\text{Length of triangle D}} = \frac{1.6}{4.8} \]

Now, we can simplify the fraction:

\[ \frac{1.6}{4.8} = \frac{1.6 \div 1.6}{4.8 \div 1.6} = \frac{1}{3} \]

Thus, the scale factor is \( \frac{1}{3} \), which corresponds to "one third" from the options given.

Final answer: one third.