To find the length of AB, we can use the Pythagorean theorem.
Assuming AC is the hypotenuse, we can set up the equation:
AD^2 + BD^2 = AC^2
7^2 + BD^2 = 13^2
49 + BD^2 = 169
BD^2 = 120
BD = √120
BD = 2√30
Now, since BD is the altitude to the hypotenuse, it divides the hypotenuse AC into two segments in the ratio of the adjacent sides of the triangle. Therefore:
AB/BD = AD/DB = 7/2
AB/2√30 = 7/2
AB = 7√30
So, the length of AB in simplest radical form is 7√30.
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, 7AD=7 and A, C, equals, 13, commaAC=13, what is the length of start overline, A, B, end overline
AB
in simplest radical form?
1 answer