Question

Find the dimensions of a rectangular enclosure with perimeter 40 yd and are 91 yd^2

Answer 1

Let the length be x.

Width = Perimeter /2 - x = 20 - x.


Area = length x width = (20 - x) = 20x - x^2 = 91.


x^2 - 20x + 91 = 0.

(x - 7) (x -13) = 0.

x = 7 or 13.

ANSWER: Length = 13yds Width = 7 yds.

Answer 2

thank you

Answer 3

You're welcome!! Xo!

Answer 4

wait so its a rectangle so perimeter/2 how do you know it gives you the length not the width or does it matter

Answer 5

doesn't matter

Answer 6

Im slightly confused still can you go through all of the steps i have a huge test tomarrow lol

Answer 7

ok so a rectangle has 4 sides, correct? 2 sides for width and 2 for length.

Answer 8

yes.

Answer 9

so perimeter should be equal to 2 width + 2 length

Answer 10

yea.

Answer 11

and area is equal to length times width

Answer 12

well yea i just dont know what to do with the numbers

Answer 13

ok well think about it this way…. whats half of the perimeter? L+W=20 right?

Answer 14

so if you try to solve for width you'll get W = 20-L

Answer 15

so say perimeter equals 34ft and area equals 60ft^2
width=perimeter/2-x again?

Answer 16

so length is = L
and width is = 20-L

if we fill this into our area formula we get….
area = L(20-L)
we know area is 91 yrds^2
91 =L(20-L)

Answer 17

yes, you're correct… the reason why we divide it is so we don't have to work with 2 sides, as long as you remember we have used half the perimeter, its fine.

Answer 18

so 60=17l-l^2 for the problem i just said

Answer 19

yes

Answer 20

and then 60/17 leaves me with 3.5=l-l^2?

Answer 21

no, you can't do that… if you're dividing you have to be able to take it from all terms on each side…. bring your 60 over to the other side like this…

0 = -60+17L-L^2

Answer 22

then factor to get (12+L)(7+L)??

Answer 23

right

Answer 24

close.. what adds to give you -17 and multiplies to give you +60?

Answer 25

12 and 5 i mean

Answer 26

they would have to be negative… remember the - in front of L^2

Answer 27

but you are correct (L-5)(L-12)

Answer 28

okay thank you so much i think i understand now

Answer 29

great! good luck on your test. Practice really makes perfect with this stuff.

Answer 30

one more question if it is not factorable can i use the quadratic formula

Answer 31

yes