In an isosceles triangle, the base is 18 cm and the side is 41 cm. Find the height of the triangle.

Given: an isosceles triangle, the base of the triangle is 18 cm, the side is 41 cm.

Find: the height of the triangle (h).

Solution: lower the height to the base;

the height in an isosceles triangle is also the median, that is, it divides the base into two equal segments, 18: 2 = 9 cm.

Consider a right-angled triangle with a 9 cm leg and a 41 cm hypotenuse, we need to find the second leg, which is the height of this triangle. Let’s use the Pythagorean theorem: in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the legs.

41 ^ 2 – 9 ^ 2 = 1,600; h = 40 cm.

Answer: 40 cm is the height of the triangle.