Question

A rectangular garden has an area of 80m^2. Its length is 2 meters longer than its width. How much fencing is needed to enclose the garden

Answer 1

Explanation:

Formula

A = L * w

P = 2*L + 2*w In Effect, you are trying to find P

Givens

A = 80 m^2

w = x

L = x + 2

Solution

x*(x + 2) = 80 Remove brackets

x^2 + 2x = 80 Subtract 80 from both sides

x^2 + 2x - 80 = 80-80 Combine

x^2 + 2x - 80 = 0 Factor the quadratic

(x - 8)(x + 10) = 0

x + 10 is an extraneous solution: x would = -10 which can't exist

x - 8 = 0

x = 8

w = 8

L = 8 + 2 = 10

L = 10

Fencing

P = 2L + 2w

P = 2*10 + 2*8

P = 20 + 16

P = 36 meters

Answer

36 meters of fencing is needed