The length of a certain rectangle is to its width as 8 to 5 and the number of square feet in its area is equal to the number of linear (rest in description)

Question

Feet in its perimeter less three. Find it's length and width

how do I solve this

Answer 1

Okay, area = three less than perimeter.

So here's what we know:

A_rec = lw

P_rec = 2l + 2w

l:w = 8:5, or for every 8 of length, there's 5 width

 

P = 2 * 8x + 2 * 5x

P = 16x + 10x

P = 26x

 

A = 8x * 5x

and

A = P - 3

 

So we have:

40x² = 26x - 3

40x² - 26x + 3 = 0

 

Let's try using the quadratic formula to get our answer. It's not pretty, sure, but would you rather try out ALL of the various factors 40 can give you?

 

x= (-b ± √(b² - 4ac))/2a

x= (26 ± √((-26)² - 4 * 40 * + 3) / 2*40

x= (26 ± √(676 - 480))/80

x= (26 ± √196)/80

x=  (26 ± 14)/80

 

x= (26+14)/80

x = 40/80

x = 1/2

 

x = (26 - 14)/80

x = 12 / 80

x = 3/20

 

If those are our Xs, then let's try plugging them into our area and perimeter formulas way back at the beginning:

P = 26 * 1/2 = 13

 

A = P - 3 --> 13 - 3 = 10

 

Checking our answer:

A = 8*(1/2) * 5(1/2)

A = 4 * 5/2

A = 2 * 5

A = 10

So length being 4 and width being 5/2 (or 2.5) feet works.