A rectangle is twice as long as it is wide. If its length and width are both decreased by 4 cm, its area is decreased by 164 cm. What are the original dimensions?

2 Answers
Douglas K.
Dec 22, 2017

#W = 15" cm"#

#L = 30" cm"#

Explanation:

A rectangle is twice as long as it is wide.

#L = 2W#

If its length and width are both decreased by 4 cm, its area is decreased by 164 cm.

#(L-4" cm")(W-4" cm") = "Area"-164" cm"^2#

We know that #"Area: = LW#

#(L-4" cm")(W-4" cm") = LW-164" cm"^2#

Substitute #2W# for #L#

#(2W-4" cm")(W-4" cm") = 2W^2-164" cm"^2#

Multiply the binomials, using the F.O.I.L. method:

#2W^2-8" cm"W-4" cm"W + 16" cm"^2 = 2W^2-164" cm"^2#

#-12" cm"W = -180" cm"^2#

#W = 15" cm"#

#L = 30" cm"#

Jim G.
Dec 22, 2017

#"length "=30" cm "," width "=15" cm"#

Explanation:

#color(blue)"Original rectangle"#

#"let the width "=x#

#"then length "=2x#

#"and area "=2x xx x=2x^2#

#color(blue)"Revised rectangle"#

#" width "=x-4#

#"length "=2x-4#

#"area "=2x^2-164#

#"now "(x-4)(2x-4)=2x^2-164#

#rArrcancel(2x^2)-12x+16=cancel(2x^2)-164#

#rArr-12x=-180#

#rArrx=(-180)/(-12)=15#

#color(blue)"Original rectangle"#

#"width "=x=15" cm "#

#"length "=2x=(2xx15)=30" cm"#

#color(magenta)"As a check"#

#"original area "=15xx30=450" square cm"#

#"revised area "=11xx26=286" square cm"#

#"difference in area "=450-286=164" square cm"#

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