Answered

In triangle ABC, the measure of angle B is 90 degree and BD is an altitude of the triangle. The length of AB is 15 and the length of AC is 23 greater than the length of AB. What is the value of BC/BD ?



Answer :

sqdancefan

Answer:

  38/15

Step-by-step explanation:

You want to know the ratio BC/BD in right triangle ABC with BD the altitude to the hypotenuse, AB=15 and AC=AB+23.

Similar triangles

The right triangles in this figure are similar to each other:

  ∆ABC ~ ∆BDC ~ ∆ADB

This means the sides are proportional:

  [tex]\dfrac{BC}{BD}=\dfrac{AC}{AB}=\dfrac{15+23}{15}\\\\\\\boxed{\dfrac{BC}{BD}=\dfrac{38}{15}}[/tex]

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