Find the perimeter of an isosceles triangle in which the height to the base is 5 cm and the area is 60 cm.

Area of a triangle:

S = ah / 2, where a is the base, h is the height.

a = 2S / h = 120/5 = 24 cm.

The height dropped to the base of the isosceles triangle will also be the median. Therefore, she will divide the triangle into two right-angled triangles with legs, which will be equal to half of the base a / 2 = 24/2 = 12 cm and height h = 5 cm.

The side for these triangles will be the hypotenuse:

b = √ (a ^ 2 + h ^ 2) = √ (12 ^ 2 + 5 ^ 2) = √169 = 13 cm.

Perimeter of a triangle:

p = 2b + a = 2 * 13 + 12 = 38 cm.

Answer: 38 cm.