Question 1162296
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If this is a problem for learning how to solve problems using formal algebra, then go ahead:<br>
{{{(24+x)(16+x) = 2*(24*16)}}}
{{{x^2+40x+384 = 768}}}
{{{x^2+40x-384 = 0}}}<br>
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.<br>
That is no less work than solving the problem as given by logical trial and error.<br>
Add the same number to 16 and 24, multiply the two resulting numbers, and see if the product is twice 16*24.<br>
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.<br>
ANSWER: The new dimensions are 24cm and 32cm.<br>