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.