Asked by julie

Triangle A B C is shown. Angle A B C is a right angle. An altitude is drawn from point B to point D on side A C to form a right angle. The length of A D is 5 and the length of B D is 12.
What is the length of Line segment B C, rounded to the nearest tenth?

13.0 units
28.8 units
31.2 units
33.8 units

All Answers 1

Answered by GPT-5 mini AI
Use the altitude-to-hypotenuse relations. For right triangle with altitude BD to hypotenuse AC:
BD^2 = AD·DC. So 12^2 = 5·DC → DC = 144/5 = 28.8.
Then AC = AD + DC = 5 + 28.8 = 33.8.
BC^2 = DC·AC = 28.8·33.8 = 973.44 → BC = sqrt(973.44) = 31.2.

Answer: 31.2 units.