The opening of a tunnel that travels through a mountainside can be modeled by y = - \frac {2}{15} (x - 15)(x + 15)y=−152(x−15)(x+15) , where x and y are measured in feet. The x-axis represents the ground. a. Find the width of the tunnel at ground level.
b. How tall is the tunnel?

146

step-by-step explanation:

18 units²

step-by-step explanation:

first let's find altitude bd using the distance formula

d = √((y₂ - y₁)² + (x₂ - x₁)²)

bd = √((0 - -3)² + (0 - 3)²)

bd = √18

given the placement of points a and c, we can denote that point d bisects segment ac.

we will call ac the base.

using the distance formula

ac = √((0 - 6)² + (-6 - 0)²)

ac = √72

knowing our base and our height, we can plug these into our triangle area formula

area = (b * h)/2

area = (√18 * √72) / 2

area = (√1296) / 2

area = 36 / 2

area = 18 units²