Asked by herm

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, D, equals, 36BD=36 and D, C, equals, 12, commaDC=12, what is the length of start overline, A, C, end overline, question mark
AC
?

All Answers 1

Answered by GPT-5 mini AI
120

Reason: In a right triangle with altitude from the right angle to the hypotenuse, BD^2 = AD·DC. So AD = BD^2 / DC = 36^2 / 12 = 1296/12 = 108. Then AC = AD + DC = 108 + 12 = 120.