ALGEBRA HELP PLEASE!!!! Here's A TOUGH ONE!!!! PLEASE HELP, THANK YOU!?

Question

Ok,here's the question:

The Perimeter of a rectangular concrete slab is 114 feet and its area is 722 square feet. What is the length of the longer side of the slab???

It would help me a ton if you would explain how you got your answer since ive been thinking this through a lot and I can't solve it, Please help me, thank you so much!

Answer 1

38 and 19 are the 2 side lenghts... i used guess and check.. find 2 numbers that multiply to equal 722 then see if they also add up to 114 for the perimeter 19*38=722  2(19+38)=114

Answer 2

all you do is you take 2 sets of #s that add up to 114 and on # from each set would multiply up to 722.  Guess and check mate.

Answer 3

the shorter side is 19 ft long and the longer side is 38 ft long :)

Answer 4

2l +2w = 114   l + w = 57

lw = 722   l = 722/w   Substitute this value in for l in the top equation.

722/w + w = 57   Multiply through by W to get rid of the denom.

722 + w^2 = 57w   Subtract 57w from both sides and rearrange.

w^2 - 57w + 722 = 0

(w - 19)(w - 38) = 0

So w = 19 or w = 38

Then l = 38 or l = 19

Either way, one side is 38 and the other is 19.

Answer 5

Area = Length*Width (A=LW) so...

722=LW

Since it's a rectangle, you know that the perimeter is going to equal the four sides added together. Two of these sides are reffered to as the "Length" and the other two as the "Width." So 114= 2L+2W.

You now combine your two equations solving for W in terms of L using the first equation. This gives you: W= 722/L. You now have 114= 2L + 2(722/L). i would now solve this on a graphing calculator by placing 114 into Y1 and 2L + 2(722/L) into Y2.  You find the point of intersection by going to Calc 5 and it gives you L= 38

Answer 6

ok here goes

let L is the length of the rectangle and W be the width.

Perimeter would be equal to 2 X (L+W) = 114   ------> eq 1

Area would be equal to L x W = 722  ----> eq 2

rearranging eq 2 gives  L = 722 / W

substituting it to eq 1 gives

    2 x (722/W+W) = 114

then to simplify

    722/W +W = 57

    722 / W = 57 - W

    722 = 57W - W^2

gives a quadratic equation

  solve by factoring

   (W - 19) (W - 38) = W^2 - 57W +722

      W = 19, L = 38