A rectangular garden has an area of 120 square feet. If the width of the garden is 2 less feet than the length of the garden, what are the width and length of the garden?

1 Answer
Jan 28, 2018

Answer:

Length : #12# feet

Width : #10# feet

Explanation:

Let the length of the garden be #x# feet.

Therefore, the breadth or width of the garden is #(x - 2)# feet.

So, According to the problem,

#x(x - 2) = 120#

#rArr x^2 - 2x = 120#

#rArr x^2 - 2x - 120 = 0# [Transposing 120 to the L.H.S]

#rArr x^2 + 10x - 12x - 120 = 0# [Breaking #-2x# as #10x - 12x#]

#rArr x(x + 10) - 12(x + 10) = 0# [Taking the like terms aside]

#rArr (x + 10)(x - 12) = 0# [Completing the factorisation]

We know, When two real quantities are multiplied and the product is zero, then one of them or both of them should be zero.

So, Either #x + 10 = 0# or #x - 12 = 0#

So, #x = -10 or 12#

As #x# indicates length, #x# can't be negative.

So, #x = 12#.

So, The length of the garden is #12# feet and the width of the garden is #(12 - 2)# feet = #10# feet.