Math 055 word problem

Question

The area of a triangle flower bed in the park is 140 square feet. The base is 2 feet longer than twice the height. Find base and height. Round to nearest tenth.

please help with!

Answer 1

Set the height dimension of the triangle as h and your base dimension b becomes b=2+2h because the base is "two feet longer than twice the height."

Knowing that the area is 140 sqft and that the area of a triangle= bh/2 you can set up and solve your equation as such:

Area = bh/2

140= bh/2

140=((2+2h)h)/2

280=(2+2h)h

280= 2h+2h^2

2h^2+2h-280=0

Using the quadratic formula:

h= (-2 +- sqrt(4 - 4*2*-280))/(2*2)

h= 11.3427 or − 12.3427 <-- IGNORE negative h value bc you're working with dimensions

Because b=2+2h, b= 24.6854

So, height is 11.3427 ft and base is 24.6854 ft.

As a check, plug into the area formula and you'll see that bh/2 = 140 sqft!