In triangle A B C , the measure of angle B is 90 ° and B D is an altitude

Question

In triangle A B C , the measure of angle B is 90 &#176; and B D is an altitude of the triangle. The length of A B is 15 and the length of A C is 23 greater than the length of A B . What is the value of B C B D ?

Accepted Answer

Choice D is correct. It's given that in triangle A B C , the measure of angle B is 90 &#176; and B D is an altitude of the triangle. Therefore, the measure of angle B D C is 90 &#176; . It follows that angle B is congruent to angle D and angle C is congruent to angle C . By the angle-angle similarity postulate, triangle A B C is similar to triangle B D C . Since triangles A B C and B D C are similar, it follows that A C A B = B C B D . It's also given that the length of A B &#175; is 15 and the length of A C &#175; is 23 greater than the length of A B &#175; . Therefore, the length of A C &#175; is 15 + 23 , or 38 . Substituting 15 for A B and 38 for A C in the equation A C A B = B C B D yields 38 15 = B C B D . Therefore, the value of B C B D is 38 15 . Choice A is incorrect. This is the value of B D B C . Choice B is incorrect and may result from conceptual or calculation errors. Choice C is incorrect and may result from conceptual or calculation errors.

Question in-tri