SOLUTION: a rectangler is 24cm long and 16cm wide. when each dimension is increased by the same amount, then area is doubled. find the new dimensions.

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Question 1162296: a rectangler is 24cm long and 16cm wide. when each dimension is increased by the same amount, then area is doubled. find the new dimensions.
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39626) About Me  (Show Source):
You can put this solution on YOUR website!
24%2A16 based on old dimensions, area

%28x%2B24%29%28x%2B16%29=2%2A24%2A16%29-----------continue from this.

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


If this is a problem for learning how to solve problems using formal algebra, then go ahead:

%2824%2Bx%29%2816%2Bx%29+=+2%2A%2824%2A16%29
x%5E2%2B40x%2B384+=+768
x%5E2%2B40x-384+=+0

To solve this using algebra (instead of the quadratic formula), you need to find two numbers with a product of 384 and a difference of 40.

That is no less work than solving the problem as given by logical trial and error.

Add the same number to 16 and 24, multiply the two resulting numbers, and see if the product is twice 16*24.

A student with very good mental math skills might see the answer almost immediately: 32*24 is twice 16*24; and 16+8=24 and 24+8=32.

ANSWER: The new dimensions are 24cm and 32cm.