The area of a rectangular garden is 308 square meters. The width is 3 meters longer than one-half of the length. Find the length and the width of the garden?

Question

Can anyone help me out with this question?

Answer 1

Hi Amanda,

 

Let W = the width and let L = length.

 

Area = length x width--> 308 = LW

 

The width is 3 meters longer than 1/2 of the length--> W = 3 + (L/2)

 

Substitute 3 + (L/2) for W in the area equation--> 308 = L (3 +(L/2))

 

308 = 3L + (L^2/2)

 

Multiply everything by 2 to get rid of the fraction--> 616 = 6L + L^2

 

Subtract 616 from both sides--> L^2 + 6L - 616 = 0

 

Quadratic equation:  a=1    b=6    c= - 616

 

L = (-6 +/- sq root (36 + 2464)) / 2

 

L = -3 + 25      L = -3 -25 which you can forget about because you can't have a negative length.

 

So L = 22 meters

 

Then W = 14 meters

 

Dan