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.
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.
Answers
GPT-4o mini
Kara's first error is that she should have written the proportion in step 1 as \(\frac{12}{72} = \frac{14}{x}\).
In similar triangles, the corresponding sides are compared in the correct order based on their similarity. Since the side lengths from triangle VXW are related to triangle ZXY, the ratio should have the corresponding side lengths from the two triangles in the proper position.
So, the correct proportion should reflect this relationship based on the similarity of the triangles.
In similar triangles, the corresponding sides are compared in the correct order based on their similarity. Since the side lengths from triangle VXW are related to triangle ZXY, the ratio should have the corresponding side lengths from the two triangles in the proper position.
So, the correct proportion should reflect this relationship based on the similarity of the triangles.