SOLUTION: The length of a rectangle is 3 cm, and the width is 2 cm. If both the length and the width are increased by equal amounts, the area of the rectangle is increased by 14 cm^2. Find t

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: The length of a rectangle is 3 cm, and the width is 2 cm. If both the length and the width are increased by equal amounts, the area of the rectangle is increased by 14 cm^2. Find t      Log On


   

Question 1175571: The length of a rectangle is 3 cm, and the width is 2 cm. If both the length and the width are increased by equal amounts, the area of the rectangle is increased by 14 cm^2. Find the length and width of the larger rectangle.
Found 2 solutions by ikleyn, josgarithmetic:
Answer by ikleyn(52805) About Me  (Show Source):
You can put this solution on YOUR website!
.

    (2+x)*(3+x) - 2*3 = 14  cm^2


     6 + 5x + x^2 - 6 = 14


     x^2 + 5x - 14 = 0.


Factor

 
    (x+7)*(x-2) = 0.


The only positive root is x = 2.  It is the increment value.


ANSWER.  The larger rectangle dimensions are  2+2 = 4 cm (the width)  and  3+2 = 5 cm  (the length).

Solved.



Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Increase by x, for each

%283%2Bx%29%282%2Bx%29-3%2A2=14
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3%2A2%2B5x%2Bx%5E2-3%2A2=14
x%5E2%2B5x=14
x%28x%2B5%29=14=2%2A7
highlight_green%28x=2%29
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The larger rectangle dimensions are 5 length and 4 width (centimeters)