What is the base of the triangle?

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?

Answer _____cm

Answer 1

Hi Patricia

The base of the triangle is 8 cm

Given the values below for your triangle you can apply a quadratic to solve for the base.

Area = 60 = (bh)/2

Let b = the base

Let b + 7 = the height

We can start by applying the given substitution for the height in the formula for the area

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

Multiply both sides of the equation by 2

120 = b(b+7)

Remove the parentheses

120 = b² + 7b

Subtract 120 from both sides of the equation to form a quadratic

0 = b² + 7b - 120

Factor the quadratic

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

Length cannot be negative so b = -15 cannot be used

b = 8

b + 7 = 8 + 7 = 15 = h

Checking

Area = (bh)/2 = (15*8)/2 = 120/2 = 60

I hope this helps.