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
Answers
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:
[tex] \frac{AB}{XY} = \frac{BC}{YZ} = \frac{AC}{XZ} [/tex]
AB = 15
XY = 5
YZ = 12
Thus:
[tex] \frac{AB}{XY} = \frac{BC}{YZ} [/tex]
Plug in the values
[tex] \frac{15}{5} = \frac{BC}{12} [/tex]
Multiply both sides by 12
[tex] \frac{15}{5}*12 = \frac{BC}{12}*12 [/tex]
[tex] \frac{15*12}{5} = BC [/tex]
[tex] 36 = BC [/tex]
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.
[tex]\rm \dfrac{AB}{XY}=\dfrac{BC}{YZ}=\dfrac{AC}{XZ}[/tex]
Step 4 - Now, substitute the values of YZ, XY, and AB in the above expression.
[tex]\rm \dfrac{15}{5}=\dfrac{BC}{12}[/tex]
Step 5 - Simplify the above expression.
BC = 36
For more information, refer to the link given below:
https://brainly.com/question/25882965
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