document.write( "Question 523965: How do I find the height of a triangle if I am only given the length of 2 sides?
\n" ); document.write( "Problem:
\n" ); document.write( "In ΔABC, AB = 24 cm and BC = 15 cm.
\n" ); document.write( "CD bisects AB.
\n" ); document.write( "ΔCDB is a right triangle.
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #347491 by solver91311(24713) $\"\"$ $\"About$

You can put this solution on YOUR website!
\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "You are given a lot more than just the measure of two sides, though I have to simply assume that point D is on the segment

(you didn't specifically say so and you didn't provide a diagram). With that presumption, knowing that

bisects

and that

is right, then CD is a perpendicular bisector of AB. That means that

is congruent to

(by SAS) and ABC is an isosceles triangle with C as the apex and AB as the base. Further, you know that

. From that you can see that

is a right triangle with a leg that measures 12 and a hypotenuse that measures 15. You can either use Pythagoras or recognize a 3-4-5 proportion right triangle to determine that the short leg, specifically

, measures 9. From that you calculate the area by base times height divided by 2.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "John
\n" ); document.write( "

\n" ); document.write( "My calculator said it, I believe it, that settles it
\n" ); document.write( "

$\"The$

\n" ); document.write( " \n" ); document.write( "

\n" );