# 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?

##### 1 Answer

Nov 20, 2017

#### 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"#