The length of a rectangle is 10 inches more than 4 times the width. If the area of the rectangle is 336 square inches, find the length and the width.

Question

please help.

Answer 1

Let x = width, then length = 4x+10.

 

A = l x w

 

336 = x(4x+10)  put into standard form

 

4x² + 10x - 336 = 0  divide by 2

 

2x² + 5x - 168 = 0  and solve using the quadratic formula and get 

 

-21/2 and 8, the neg answer will not work, so the width = 8, length = 42

Answer 2

Length L = 4w + 10  for width w

 

Area = length x width = Lw

 

    336 = w(4w + 10)

 

   336 = 4w^2 + 10w

 

   0 = 4w^2 + 10w - 336

 

  0 = 2w^2 + 5w - 168

 

  0 = (  2w     +    21 )( w    -     8   )

 

  2w + 21 = 0   ---> w = -21/2  results in negative measures

 

w-8 = 0 ---> w = 8  

 

The width is 8.

The length is 4(8)+10 = 32+10  = 42

The area is 8 x 42  = 336