What is the length of the altitude drawn to the hypotenuse? The figure is not drawn to scale.
A large right triangle is shown. A perpendicular segment is drawn from the right angle of the large right triangle to the opposite side. That segment divides the opposite side into two parts. The segment on the left is labeled 5. The segment on the right is labeled 14.
(1 point)
Responses
Start Root 70 End Root
Image with alt text: Start Root 70 End Root
70
70
Start Root 19 End Root
Image with alt text: Start Root 19 End Root
19
We can use the Pythagorean theorem to find the length of the altitude drawn to the hypotenuse.
Let x be the length of the altitude. Then, using the two smaller triangles created by the altitude, we have:
x^2 + 5^2 = (14)^2
x^2 + 25 = 196
x^2 = 171
x = √171
Therefore, the length of the altitude drawn to the hypotenuse is √171.