The area of a triangle, the base of which is 20 cm greater than the height, is 78 cm². Find the base of the triangular.

Let’s compose an equation in which we write the value of the height of the triangle as x cm.

Since the side of the base is 20 cm larger, its value will be: x + 20 cm.

The area of a triangle is the product of its two sides by 1/2, so we get:

1/2 * (x * (x + 20)) = 78.

1/2 * (x2 + 20 * x) = 78.

0.5 * x2 + 10 * x – 78 = 0.

x2 + 20 * x – 156 = 0.

√D = 202 – 4 * 1 * (-156) = 400 + 624 = 1024.

D = √1024 = 32.

x = (-20 + 32) / 2 = 12/2 = 6 cm (triangle height).

x + 20 = 6 + 20 = 26 cm (base).

Answer: 26 cm.