Question

Triangle VXW is similar to triangle ZXY.

Triangle V X W. Side V W is 12 miles and side V X is 14 miles. Triangle Z X Y. Side Y Z is 72 miles and side X Z is x miles.

Kara finds the value of x. Her work is shown below.

Step 1 StartFraction 14 Over 72 EndFraction = StartFraction 12 Over x EndFraction

Step 2 14 x = (72) (12)

Step 3 14 x = 864

Step 4 x = 61.7

What is Kara’s first error?
Kara should have written the proportion in step 1 as StartFraction 12 Over 72 EndFraction = StartFraction 14 Over x EndFraction.
Kara should have written the cross-product in step 2 as 12 x = (72) (14).
Kara did not correctly divide 864 by 14 going from step 3 to step 4.
Kara did not find the correct product of 72 and 12 going from step 2 to step 3.

Answer 1

Kara’s first error is in Step 1. She should have written the proportion as 12/72 = 14/x (or 14/x = 12/72), since VW (12) corresponds to YZ (72) and VX (14) corresponds to XZ (x).