there are 2 90* angles with on side of the triangle being 4 and the second side of another triangle being 14 and they are both on the same side
9. Find the length of the altitude drawn to the hypotenuse. * 28 7.5 14 9
To find the length of the altitude drawn to the hypotenuse, we can use the Pythagorean theorem.
Let's consider the triangle with side lengths 4, x, and the hypotenuse.
Using the Pythagorean theorem:
4^2 + x^2 = (hypotenuse)^2
16 + x^2 = (hypotenuse)^2
Since the angle opposite the side of length 4 is 90 degrees, the altitude bisects the hypotenuse, making two smaller right triangles. Let's call the lengths of the two smaller right triangles h and 14-h.
Using the Pythagorean theorem for these two right triangles:
x^2 + h^2 = 4^2
x^2 + (14-h)^2 = 14^2
Substitute x^2 from the first equation into the second equation:
16 + h^2 + 196 - 28h + h^2 = 196
2h^2 - 28h + 16 = 0
2(h-14)(h-1) = 0
This gives us two possible lengths for h: 1 and 14.
However, the length of the altitude cannot be 1, as this would not reach the hypotenuse.
Therefore, the length of the altitude drawn to the hypotenuse is 14.
The correct answer is 14.