SOLUTION: I am not sure how to find the length and width of a rectangle, by looking at the perimeter and area. The question is "A rectangle has an area of 35 sq. ft, and a perimeter of 27 f

Question 171474: I am not sure how to find the length and width of a rectangle, by looking at the perimeter and area. The question is "A rectangle has an area of 35 sq. ft, and a perimeter of 27 ft. What is the length and width of the rectangle?"
hope you can help!! thank you.
Found 3 solutions by monika_p, josmiceli, jojo14344:
Answer by monika_p(71)   (Show Source): You can put this solution on YOUR website!
Formula for area of rectangle is A= a*b
Formula for perimeter of rectangle is P=2a+2b
where a and b are the sides of rectangle
You have given A=35sq ft and P= 27 ft, then
a*b = 35
2a+2b = 27
Now solve system of two equations
From first equation we have a=35/b,
then second equation:
2*(35/b) +2b =27 , now multiply both sides by b
2*35 +2b^2=27b
2b^2-27b+70=0 quadratic equation (Ax^2+Bx+C=0)
A=2, B=-27, C=70
find discriminant B^2-4AC = 169 > 0 equation has 2 solutions

b1=3.5

b2=10

a = 35/b then for b1=3.5 ---> a1=10 and for b2=10---> a2=3.5
We got set of two the same numbers then lets a=10ft and b=3.5ft
Prove : A = 10*3.5 =35 and P= 2*10+2*3.5=27

Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
First, choose symbols for the width and length
width =
length =
The area of the rectangle is
The problem gives me ft2, so

The formula for the perimeter is obtained by
adding up the lengths of the 4 sides, knowing
that the opposite sides are equal

The problem gives me ft, so

Now I've got 2 equations and 2 unknowns, so they're
solvable

divide both sides by

Now substitute

Multiply both sides by

Use the quadratic equation to solve

where

and also

Now which answer makes sense?
If

Does the perimeter = ?

OK
The other answer works, too, and is more
appropriate since it makes the width shorter

Answer by jojo14344(1513)   (Show Source): You can put this solution on YOUR website!

, EQN 1
we get,
---> , EQN 2
Also,
, subst. EQN 2,

--->
---> follows a quadratic eqn:
where ---->
note:

2 values:
, or

Width (either/or)---->
For Length, as per EQN 2:

LENGTH (either/or)---->
We'll check using: & :

, good

, good
*Note: either you use or will just be the same. Same thing on the
Thank you,
Jojo
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