# The area of a right-angled triangle is 150, and one of the legs is 15. What is the height dropped

**The area of a right-angled triangle is 150, and one of the legs is 15. What is the height dropped from the top of the right angle**

Let’s find the length of the second leg of this triangle.

We denote it by x.

Using the formula for the area of a right-angled triangle, we can compose the following equation:

x * 15/2 = 150,

solving which, we get:

x * 15 = 2 * 150;

x * 15 = 300;

x = 300/15 = 20.

Using the Pythagorean theorem, we find the length of the hypotenuse from a given triangle.

c = √ (15 ^ 2 + 20 ^ 2) = √ (225 + 400) = √625 = 25.

Find the length of the height dropped from the top of the right angle.

We denote it by h.

Using the formula for the area of a triangle, we can write the following equation:

h * 25/2 = 150,

solving which, we get:

h * 25 = 150 * 2;

h * 25 = 300;

h = 300/25 = 12.

Answer: The height dropped from the top of the right angle is 12.