Question

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.

Answer 1

MRCORRECT has answered the question

Explanation:

Base = b

height =h = b+7

Area = 1/2 * b* h

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

120 =b2+7b

b2+7b-120=0

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

b=-15 and b=8

base cannot be negative

so base =b =8 cm

Answer 2

8 cm

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.