Length and width of garden

Question

The area of a rectangular is 105 square meters. The width is 2 meters longer than one-third of the length. Whatso the length and width?

Answer 1

The area is 105 sq meters...

Area of a rectangle is Length * Width or LW so

 

LW = 105

 

Width is 2 m longer than 1/3 of the length so

W = L/3 + 2

 

Substituting L/3 + 2 in place of W in LW=105 we get

 

L(L/3 + 2) = 105

L²/3 + 2L = 105

multiply through by 3 to eliminate the fraction

L² + 6L = 315

L² + 6L - 315 = 0

This can be factored.  The factors of -315 that

add to 6 are 21(-15)

L²+6L-315 = 0

(L+21)(L-15)=0

L = -21 or L = 15

Eliminating the negative, we have the length is

L = 15 meters

 

The width is 15/3 + 2 = 5+2=7 meters

 

The rectangle is 15m by 7m

 

Area = LW = 15(7) = 105 sq meters