The base of a straight triangular prism is a right-angled triangle with legs 5 and 12, its surface area

The base of a straight triangular prism is a right-angled triangle with legs 5 and 12, its surface area is 120. Find the height of the prism.

As you know, the area of the lateral surface of a straight prism is equal to:

S = P * h, where P is the perimeter of the base and h is the height of the prism.

To find the perimeter of the base, we need to find the length of its third side.

Since the base is a right-angled triangle, the legs of which are known, we find its hypotenuse using the Pythagorean theorem.

Let the hypotenuse be equal to x, we get:

х² = 5² + 12²,

x² = 25 + 144,

x = 13.

Thus, the perimeter of the base of the prism is:

P = 12 + 5 + 13 = 30.

Therefore, h = 120: 30 = 4.