Given right triangle A, B, CABC with altitude start overline, B, D, end overline

Question

BD
drawn to hypotenuse start overline, A, C, end overline
AC
. If A, D, equals, 5AD=5 and D, C, equals, 5, commaDC=5, what is the length of start overline, B, D, end overline, question mark
BD
?

Answer 1

Let's call the length of the hypotenuse AC = x.
Since AD = 5 and DC = 5, we can consider the two smaller triangles ABD and CBD.

In triangle ABD:
Using the Pythagorean Theorem, we have:
BD^2 + 5^2 = x^2
=> BD^2 + 25 = x^2

In triangle CBD:
Using the Pythagorean Theorem, we have:
5^2 + BD^2 = x^2
=> 25 + BD^2 = x^2

Since both expressions equal x^2, we can set them equal to each other:
BD^2 + 25 = 25 + BD^2
=> BD^2 + 25 = BD^2 + 25

This means that BD = 5.

Therefore, the length of BD is 5.