Question

A rectangular picture measuring 3in by 8in is surrounded by a frame with uniform width x. Write a quadratic function in standard form to show the combined area the picture and frame

Answer 1

Let me draw the situation here below:

Ok, so:

From the figure, we can notice that the big size of the outside rectangle measures 8 + 2x.

And, the outer width is 3 + 2x.

Then, let the area be "y".

Now, y = (8 + 2x) (3 + 2x).

And this is y = 24 + 16x + 6x + 4x².

Therefore, y = 4x² + 22x + 24