A rectangular garden has a width of 5 feet and a length of 10 feet. If an equal amount is added to both the width and the length, the area is increased to 104 square feet. What is this amount?

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Answer 1 · 2017-05-06T06:23:35

The amount of increase is #3# feet.

Let us consider the amount of increase of width and length as #x#. That will make the width (#x+5#) and the length (#x+10#).

Since the formula for area of a rectangle is:

#A=lxxw#, where #A=#Area, #l=#length, and #w=#width,

with the given data we can write (reversing the equation to #lxxw=A#):

#(x+10)(x+5)=104#

#x^2+15x+50=104#

Subtract #104# from each side.

#x^2+15x-54=0#

Factorise.

#x^2+18x-3x-54=0#

#x(x+18)-3(x+18)=0#

#(x-3)(x+18)=0#

#x-3=0# or #x+18=0#

#x=3# or #x=-18#

Since the increase must be a positive integer, the amount of increase is #3#.

We check this by calculating the area:

#A=lxxw#

#A=(x+10)(x+5)#

#A=(3+10)(3+5)#

#A=13xx8#

#A=104#