At the base of a straight prism lies a right-angled triangle with legs 6 and 8 cm Find the lateral

At the base of a straight prism lies a right-angled triangle with legs 6 and 8 cm Find the lateral edge of the prism if its lateral surface is 120 cm ^ 2

a = 6 cm.

b = 8 cm.

Side = 120 cm ^ 2.

h -?

1) Find the third side c of a right-angled triangle, which is the hypotenuse, according to the Pythagorean theorem.

c = √ (a ^ 2 + b ^ 2).

c = √ ((6 cm) ^ 2 + (8 cm) ^ 2) = √100 = 10 cm.

2) The area of the lateral surface of a straight prism S side is determined by the formula: S side = (a + b + c) * h.

h = S side / (a + b + c).

h = 120 cm ^ 2 / (6 cm + 8 cm + 10 cm) = 5 cm.

Answer: the lateral edge of the prism is h = 5 cm.