the area of a rectangular garden is 140 square meters. The width is 3 meters longer than one-half of the length. Find the length and the width of the garden

Question

the area of a rectangular garden is 140 square meters. The width is 3 meters longer than one-half of the length. Find the length and the width of the garden.

Answer 1

Area of a rectangle is length times width... A = LW

 

LW = 140

W = L/2 + 3

 

Replace W with L/2 + 3 in first equation and solve for L

 

L(L/2 + 3) = 140

L²/2 + 3L = 140

multiply through by 2

L² + 6L = 280

L² + 6L - 280 = 0

 

Factors of -280 that add to 6 are 20(-14)

 

(L+20)(L-14) = 0

L = -20  or  L = 14

 

Discarding the negative, the length is 14 meters

 

W = L/2 + 3 = 10 meters

 

The garden is 14 by 10 meters