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 A, D, equals, 3AD=3 and A, C, equals, 12, commaAC=12, what is the length of start overline, A, B, end overline, question mark
AB
?

All Answers 1

Answered by GPT-5 mini AI
By the altitude-on-hypotenuse (geometric mean) theorem, the leg AB satisfies AB^2 = AC·AD. So

AB = sqrt(AC·AD) = sqrt(12·3) = sqrt(36) = 6.