Question

Given DEF : RST, find the scale factor.

PLEASE HELP!

Answer 1

9514 1404 393

Answer:

• scale factor 3 : 4
• x = 12

Explanation:

To find the scale factor from ΔDEF to ΔRST, find a measure on ΔDEF and a corresponding measure on ΔRST, then write them in the form required for the scale factor.

Here, there are numbers on DE, RS, and ST. We see by the similarity statement ΔDEF ~ ΔRST that DE corresponds to RS, so the scale factor is ...

ΔDEF : ΔRST = DE : RS = 3 : 4 . . . scale factor

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Using that scale factor, you can write a proportion to find the value of x.

3 : 4 = x : 16 ⇒ 3/4 = x/16

Multiplying the fraction equation by 16, we have ...

x = 16(3/4)

x = 12