Question

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

Answer 1

Answer:

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:

$\frac{AB}{XY} = \frac{BC}{YZ} = \frac{AC}{XZ}$

AB = 15

XY = 5

YZ = 12

Thus:

$\frac{AB}{XY} = \frac{BC}{YZ}$

Plug in the values

$\frac{15}{5} = \frac{BC}{12}$

Multiply both sides by 12

$\frac{15}{5}*12 = \frac{BC}{12}*12$

$\frac{15*12}{5} = BC$

$36 = BC$

Answer 2

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

Given :

• Angle X congruent to angle A and angle Y congruent to angle B.
• XY = 5 , YZ = 12 , and AB = 15.

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.

$\rm \dfrac{AB}{XY}=\dfrac{BC}{YZ}=\dfrac{AC}{XZ}$

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

$\rm \dfrac{15}{5}=\dfrac{BC}{12}$

Step 5 - Simplify the above expression.

BC = 36

For more information, refer to the link given below:

https://brainly.com/question/25882965