You are making a rectangular fence. The length is four less then 3 times the width.

Question

Write a polynomial that represents the area of the rectangular fence

Find the area of the fence when the width is 20 yards.

Answer 1

First, rewrite what is given into math terms.

The length is four less than 3 times the width.

length = l

four less = -4

3 times = 3x

width = w

so l= 3w-4

Part 1: Write a polynomial that represents the area of the rectangular fence.

The area for a rectangle is A=lw

substitute what is given to us above into the equation for Area

so A=(3w-4)w

distribute and simplify -> A=3w²-4w

that is our polynomial!

Part 2: Find the area of the fence when the width is 20 yards.

Given to us now is that w=20 yrds

plug this in to our polynomial to find A (area)

A=3(20)²-4(20)

20²=400*3=1200

4*20=80

1200-80=1120= A

Dont forget units! given to us in yards (yd) and we are squaring the unit so the final unit is yd²

1120 yd²

^{Please excuse my poor math at the end of the video! 4*20 is 80 not 800 (oops) everything else is correct!}

Answer 2

w = width

length = 4 less than 3 times width = 3w - 4

area = length * width = w * (3w-4)

when w = 20:

20* (3 * 20 - 4) = 1120