Question

A triangle with an area of 60 square inches has a height that is 16 less than 6 times its base.

Answer 1

Step-by-step explanation:

the area of a triangle

baseline × height / 2

in our case

baseline × height / 2 = 60 in²

height = 6×baseline - 16

baseline × (6×baseline - 16) / 2 = 60

baseline × (3×baseline - 8) = 60

3×baseline² - 8×baseline = 60

baseline = x

3x² - 8x - 60 = 0

general solution to a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

a = 3

b = -8

c = -60

x = (8 ± sqrt(64 - 4×3×-60))/(2×3) =

= (8 ± sqrt(64 + 720))/6 = (8 ± sqrt(784))/6 =

= (8 ± 28)/6

x1 = (8 + 28)/6 = 36/6 = 6

x2 = (8 - 28)/6 = -20/6 = -10/3

x2 as a negative number is not a valid solution for a length in a geometric shape.

so, x = 6 in is our solution for the baseline.

height = 6x - 16 = 6×6 - 16 = 36 - 16 = 20 in

base = 6 in