In the accompanying diagram of triangle XYZ and triangle ABC, angle X cong angle A and angle Y cong angle B . If XY = 5 , YZ = 12 , and AB = 15 , what is BC? A 15X 5 Y12B с

The length of the segment BC is 36 and this can be determined by using similar triangle properties and the given data.

Given :

The following steps can be used in order to determine the length of the segment BC:

Step 1 - According to the given data, XY = 5 , YZ = 12 , and AB = 15. Also angle X congruent to angle A and angle Y congruent to angle B.

Step 2 - So, according to the given data, it can be concluded that both the triangles are similar.

Step 3 - From the above steps, it can be concluded that the corresponding sides ratios of the triangles are equal.

Step 4 - Now, substitute the values of YZ, XY, and AB in the above expression.

Step 5 - Simplify the above expression.

BC = 36

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BC = 36

Step-by-step explanation:

If <X ≅ <A, and <Y ≅ B, therefore ∆XYZ is similar to ∆ABC.

Since ∆XYZ is similar to ∆ABC, it follows that the ration of their corresponding side lengths would be equal.

That is:

AB = 15

XY = 5

YZ = 12

Thus:

Plug in the values

Multiply both sides by 12

the correct answer is 5 6 and 7