the area of a rectangle is give by the equation 2L^2 + 5L=12, what is the length?

Question

length of rectangle

Answer 1

2L^2 +5L-12=0

 

Factor to get

 

(2L -3)(L+4)=0

2L-3=0

L=3/2=1.5

Answer 2

The area of the rectangle is 

 

2L²+5L = 12

 

 

We can rewrite this as 2L² + 5L - 12 = 0 and solve for L

 

        -5 ± √[5² - (4)(2)(-12)]

L =   ---------------------------

                    2(2)

 

        -5 ± √(25+96)

L =  ------------------

                4

 

L = (-5 ±√121)/4 = (-5±11)/4 = 6/4, -4

 

We discard the L = -4 solution since a measurement cannot realistically be a negative.

L = 6/4 = 3/2.

 

Normally I would think that L is the length, but let's look at one more thing

 

2L² + 5L = 12

and A = LW

 

If we factor out an L from the left side of the equation, we have

L(2L + 5) = 12

 

A = 12

L = L

2L + 5 = W = 2(3/2)+5 = 8

 

Given that length is typically greater than width, then I would say that the length is 8, unless there is something in the problem, not stated here, which states that L = length.