# The legs of a right-angled triangle are 10 and 24. Find the height drawn to the hypotenuse.

Let us denote the length of the height drawn to the hypotenuse in a given right-angled triangle by h.

Using the Pythagorean theorem, we find the hypotenuse from a given right-angled triangle:

c = √ (10 ^ 2 + 24 ^ 2) = √ (100 + 576) = √676 = 26.

Since the leg in a right-angled triangle is also the height of this right-angled triangle, drawn to the other leg, the area S of a right-angled triangle is half the product of the lengths of the legs:

S = 10 * 24/2 = 120.

At the same time, the area of a right-angled triangle is equal to half the product of the length of the hypotenuse and the height drawn to the hypotenuse of this right-angled triangle, therefore, the following relationship is true:

h * 26/2 = 120.

We solve the resulting equation:

h * 13 = 120;

h = 120/13;

h = 9 3/13.

Answer: The length of the height drawn to the hypotenuse is 9 3/13.