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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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