SOLUTION: The length of a rectangle is 7 feet longer than it is wide. If each side is increased 7 feet then the area is multiplied by 2. What was the size of the original rectangle?

Algebra ->  Rectangles -> SOLUTION: The length of a rectangle is 7 feet longer than it is wide. If each side is increased 7 feet then the area is multiplied by 2. What was the size of the original rectangle?       Log On


   

Question 1166191: The length of a rectangle is 7 feet longer than it is wide. If each side is increased 7 feet then the area is multiplied by 2. What was the size of the original rectangle?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
length w+7
width w

%28w%2B7%2B7%29%28w%2B7%29=2w%28w%2B7%29
.
.

Answer by ikleyn(52782) About Me  (Show Source):
You can put this solution on YOUR website!
.

Let the width be w feet;

Then the length  is (w+7) feet


The condition says

    (w+7+7)*(w+7) = 2w(w+7).


At this point, do not make FOIL.

Do not create a quadratic equation --- there is a simpler way.

Cancel the common factor (w+7) in both sides.  You will get then


    w + 7 + 7 = 2w

    w + 14    = 2w

    w = 14.


So, the dimensions of the original rectangle are  14 ft (the width)  and  14+7 = 21 ft (the length).

Solved.

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You may also think,  what the condition means,  geometrically.

Thinking in this way,  you will be able to solve the entire problem  MENTALLY  (in your head).