Question 1046667

given:
A square garden is to be enlarged to a rectangular by adding {{{5ft}}}, to the length and deducting {{{4ft}}}. 
 the area will be unchanged

to find:  present and new dimensions

as you know, the area of a square is
{{{A= length * width}}}

Let {{{s}}} = side of square

so, the area is {{{A=s^2}}}........eq.1

now you want to make a rectangle from that square by adding {{{5ft}}} to the {{{s}}} and  the width reducing {{{s}}} by {{{4ft}}} 

so, rectangle will have:
the length: {{{(s + 5)}}}
Width: {{{(s - 4)}}}

the area of rectangle will be:
{{{A=(s + 5) (s - 4)}}}...expand 
{{{ A= s*s + 5*s - s*4-5*4}}}
 {{{A= s^2 + 5s - 4s-20}}}
{{{A= s^2 + s -20}}}.............eq.2

now we have:
A=s^2.............eq.1
A= s^2 + s -20.............eq.2
__________________________

since area is unchanged, left sides are equal; so, make equal right sides and solve for {{{s}}}

{{{s^2=s^2 + s -20}}}.....move all terms from right to the left

{{{s^2-s^2 - s +20=0}}}

{{{- s +20=0}}}

{{{20=s }}}

{{{s=20 }}}

so, when we have square, side length is 

 {{{s=20ft }}} ->present  dimensions


and area is {{{A=20ft*20ft=400ft^2}}}


when we make rectangle the length will be:

 {{{20ft+5ft=25ft}}} and 
the width will be {{{20ft-4ft=16ft}}}


{{{A=25ft*16ft=400ft^2}}}