SOLUTION: a rectangle is 5 ft longer than its width. if the lenght is shortened by 2 ft and the width is increased by 1 ft, the area remains unchanged. find the area.

Question 213072: a rectangle is 5 ft longer than its width. if the lenght is shortened by 2 ft and the width is increased by 1 ft, the area remains unchanged. find the area.
Answer by aggie_tutor(13) (Show Source): You can put this solution on YOUR website!
They trick you a little: They are asking for the area, but first you have to solve for the actual width. Fortunately this works out pretty easily. Let width above be w and rectangles A and B.
Area of rectangle A:
Width = w
Length = w + 5
Area rectangle A: (Length * Widgth) AreaA = (w)*(w+5)
Area of rectangle B:
Width = w + 1
Length = (w + 5) - 2
Area rectangel B: (Length * Width) AreaB =
Now the problem says the two areas are equal. Set each area computation equal to the other, and solve for width w.
AreaA = AreaB

Simplify with distributive property:

Combine like terms.

Subtrace the w^2 from each side to get rid of it. The square term cancels itself out, which is really convenient so we don't have to take a root of anything (!).

Subtract 4w from both sides to isolate the number 3.

Then plug in w to one of the rectangles to get the area.
AreaA = Length * Width =
Check your answer by subbing w in the other rectangle:
AreaB = Length * Width =
AreaA = AreaB !
RELATED QUESTIONS
a rectangle is 5 meters longer than its width. If thee length is shortened by 2 meters,... (answered by ptaylor)

The length of a rectangle is 4 ft more than its width. If the length is increased by 2... (answered by fractalier)

The length of a rectangle is three times its width. If the length is decreased by 20 ft. (answered by rothauserc)

rectangle's length is 5 ft more than its width. if the width is not changed & the length... (answered by JBarnum)

a rectangle has its length of 2 ft greater than its width.if the lenghth is increased by... (answered by lwsshak3)

The length of a rectangle is 2 ft longer than its width. If the perimeter of the... (answered by Alan3354)

The length of a rectangle is 2 ft longer than its width. If the perimeter of... (answered by Boreal)

the length of a rectangle is 5 ft longer than its width. if its area is 36 ft, what are... (answered by algebrahouse.com)

The lenght of a rectangle is 10 ft longer than twice the width.If the perimeter is 116 ft (answered by tommyt3rd)