Question

Given right triangle A, B, CABC with altitude start overline, B, D, end overline
BD
drawn to hypotenuse start overline, A, C, end overline
AC
. If B, C, equals, 10BC=10 and D, C, equals, 4, commaDC=4, what is the length of start overline, A, C, end overline, question mark
AC
?
x
10
4
A
B
D
C
x
Answer
Attempt 1 out of 2

x, equalsx=

Answer 1

Use the altitude-to-hypotenuse relation: in a right triangle with altitude from the right angle to the hypotenuse, the square of a leg equals the hypotenuse times the adjacent hypotenuse segment. So
BC^2 = AC · DC.
With BC = 10 and DC = 4:
100 = AC · 4 ⇒ AC = 100/4 = 25.