Question

the height of a triangle is 4 less than it’s base. The area of the triangle is 30 square inches. Find the length of the base to the nearest inch

Answer 1

10 inches

Explanation:

The formula for the triangle area is the following:

A = b * h / 2

Where b is the length of the base side and h is the height.

So, as the height is 4 less than the base, we have that:

h = b - 4

Using this value in the area equation, we have that:

A = b * (b - 4) / 2

30 = (b^2 - 4b) / 2

b^2 - 4b = 60

b^2 - 4b - 60 = 0

Using Bhaskara's formula to solve the quadratic equation, we have:

Delta = 4^2 + 4*60 = 256

sqrt(Delta) = 16

b1 = (4 + 16)/2 = 10

b2 = (4 - 16)/2 = -6 (negative value does not fit for this problem)

So the length of the base is 10 inches.