The height of a triangle is 7 cm longer than its base. The area of the triangle is 60 cm². What is the base of the triangle? Enter your answer in the box.

8 cm

Step-by-step explanation:

Let's say the height is h and the base is b. Since the height is 7 cm longer than the base, we can write:

h = b + 7

The area of a triangle is denoted by: A = (1/2) * b * h, where b is the base and h is the height. Plug in what we have:

A = (1/2) * b * h

60 = (1/2) * b * (b + 7)

120 = b² + 7b

b² + 7b - 120 = 0

Factor:

(b + 15)(b - 8) = 0

b = -15 or b = 8

Clearly, the base length can't be negative, so the base is 8.

The answer is thus 8 cm.