Question

The width and the length of a rectangle are consecutive even integers. If the width is decreased by 3 inches. then the area of the resulting rectangle is 24 square inches What is the area of the original rectangle?

Answer 1

`48" square inches"`

Explanation:

`"let the width "=n`

`"then length "=n+2`

`n" and "n+2color(blue)" are consecutive even integers"`

`"the width is decreased by " 3" inches"`

`rArr"width "=n-3`

`"area "="length "xx" width"`

`rArr(n+2)(n-3)=24`

`rArrn^2-n-6=24`

`rArrn^2-n-30=0larrcolor(blue)"in standard form"`

`"the factors of - 30 which sum to - 1 are + 5 and - 6"`

`rArr(n-6)(n+5)=0`

`"equate each factor to zero and solve for n"`

`n-6=0rArrn=6`

`n+5=0rArrn=-5`

`n>0rArrn=6`

`"the original dimensions of the rectangle are"`

`"width "=n=6`

`"length "=n+2=6+2=8`

`6" and "8" are consecutive even integers"`

`rArr"original area "=8xx6=48" square inches"`