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The best way to solve this would be to backsolve - use the answer choices, so it is quite unfortunate that you did not provide them - that's the fastest way really.
Without answer choices, You would need to build an equation for Area and one for Perimeter such as:
A+ B+A+B = Perimeter
A*B = Area
So, A+B+A+B = 46
A*B = 76
Here we can do something like this:
2A+2B = 46 or A + B = 23 and thus A = 23-B
Plug that into the other equation: (23 - B)*B = 76 or 23B - \(B^2\) = 76
You have a quadratic equation to solve at this point:
\(-B^2 + 23B - 76 = 0\)
If you had answer choices, you could plug them in and see which ones worked but we can solve it as well (just picking numbers, looks like 4 works from positive roots).
So, the answers are: B = 4 and A = 19
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