A rectangle has a length of 21 feet less than 5 times its width. If the area of the rectangle is 2600 square feet,find the length of the rectangle

Question

I need help solving it????

Answer 1

Hi,

A rectangle has a length of 21 feet less than 5 times its width. If the area of the rectangle is 2600 square feet,find the length of the rectangle

Step One: Create Let Statements

Let x= the width

Let 5x-21=the length

Step Two: Create an equation

length*width=area

(5x-21)(x)=2600

5x²-21x=2600 Distribute

5x²-21x-2600=0 Add 2600 to both sides

(5x+104)(x-25)

That means x=25 or x=-20.8

(because x-25=0   or    5x+104=0

              x=25             5x=-104

                                  x=-20.8

∴The length is 104 feet because 5x-21

                                  5(25)-21

                                   125-21

                                  104

Sincerely, 

Starlyte H.

Answer 2

Here's what we know:

A = lw (rectangle area formula)

l = 5w - 21 (length is 21 less than 5 times the width)

A = 2600 (rectangle area is 2,600 ft²)

 

Since we have values for two of our variables, let's plug them in:

2600 = w(5w - 21)

2600 = 5w² - 21w

0 = 5w2 - 21w - 2600

We now have a quadratic formula. Our factorization is going to look like:

0 = (5w ___)(w ___)

 

Now to factor out. Let's start off with 26 and 100 as a baseline and see how close we are:

2600 / 100 = 26 ↔ 26 * 100 = 2600

26 * 5 = 130

0 = (5w + 100)(w - 26)

0 = 5w2 - 130w + 100w - 2600 ≠ 5w2 - 21w - 2600, but it's very close.

 

Let's try 25 and 104, then.

2600 / 25 = 104 ↔ 25 * 104 = 2600

25 * 5 = 125

0 = (5w + 104)(w - 25)

0 = 5w2 + 104w - 125w - 2600 = 5w2 - 21w - 2600

 

So our factorization is indeed (5w + 104)(w - 25)

We can't have a negative amount for a width, so we can throw out 5w + 104.

0 = w - 25

25 feet = w

 

Now that we know w, we can solve for l:

l = 5 * 25 - 21

l = 125 - 21

l = 104 feet

 

And as we already checked earlier, 104 * 25 = 26000.