## 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 mile

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.v

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2 weeks 2021-09-09T17:23:02+00:00 2 Answers 0

1. Answer: Kara should have written the proportion in step 1 as;

Start Fraction 12 Over 72 End Fraction = Start Fraction 14 Over x End Fraction (that is 12/72 = 14/x)

Step-by-step explanation: The two similar triangles are given with the following dimensions;

Triangle VXW with side VW = 12 and side VX = 14. Also Triangle ZXY with side YZ = 72 and side XZ = x.

For two triangles to be similar, then there must be a similarity ration that is consistent with all sides in both triangles. This means if in the first triangle a side measures  1 unit and the similar side in the other triangle measures 5 units, then the ratio of similarity of corresponding sides shall be ratio 1 : 5. So for every corresponding side in the second triangle the measurement shall be times five of the side that corresponds in the first triangle.

Therefore, in triangle VXW and triangle ZXY, the corresponding sides are as follows;

VX = ZX

VW = ZY

XW = XY

What Kara did was as follows;

VX/ZY = VW/ZX

Which translates to 14/72 = 12/x

This was a wrong calculation because the side that corresponds to VX is ZX and not ZY.

The correct step should therefore have been;

VW/ZY = VX/ZX

12/72 = 14/x (Step 1)

12x = (72) (14) {Step 2}

x = 1008/12 (Step 3)

x = 84 (Step 4)