Question

Ryan is building a rectangular dog pen. The width of the pen will be 3 yards less than the length. The total area enclosed is 28 square yards.

a. Write an equation showing the area of the pen in terms of it length.
b. What is the length of the pen?
c. How many yards of fencing will he need to enclose the pen completely?

Okay so I got the formula and did l^2 - 3l - 28 = 0
and then got (l-7) (l+4) what do i do next ?

Answer 1

Since you have to write an expression in terms of the length, the first thing you need to do is choose a variable to represent the length.

You chose l. I'll write it as capital L, so we don't confuse it with capital "i".

Length: L
Width: L - 3
Area: L(L - 3)
Area is equal to 28, so we get:
L(L - 3) = 28
L^2 - 3L - 28 = 0
Factor:
(L - 7)(L + 4) = 0
So far you got it right.

Now you solve the above equation that you already factored.

The only way a product is zero is if at least one of its factors is zero, so you set each factor equal to zero:

(L - 7)(L + 4) = 0
L - 7 = 0 or L + 4 = 0

Now you solve each equation.

Answer 2

does L = 7 ?

Answer 3

Yes.
From the two equations, you get
L = 7 or L = -4
The L = -4 solution has to be discarded since the length of a rectangle cannot be a negative number.
That means the solution you get to the equation is L = 7

Answer 4

Now using the length, find the width.
Then with the length and width, you can calculate the perimeter and answer part c.

Answer 5

22 yards ?

Answer 6

Correct.

Answer 7

thankss

Answer 8

You're welcome.