The width of a rectangle is 2 feet shorter than its length. If its width is decreased by 1 foot and its length is increased by 4 feet, its area would be increased by 21 square feet. What is the width of the rectangle?

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w=2f shorter than length

width decreased by 1 foot and length increased by 4 area increases by 21 square foot

let length be l and width w

w=L-2

Original area= L(L-2)

(w-1) x (L+4) =L(L-2) +21

Plugin the value of w in to the equation

(L-2-1) x (L+4)=L(L-2) +21

(L-3) x (L+4) =L^2 -2L +21

L^2 +4L -3L-12=L^2 -2L +21

Group like terms together

L^2 - L^2 +L+2L=34

3L=33 ft

L=11 foot

w=11-2

=9 foot

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