First state what is known:

Large Area (A)= 270 sq in

I'm a little confused with the reference to the frame "from wall to wall" but think you mean that the frame itself is 4 inches wide all round which means that the length and width of the painting would be 8 inches smaller than the frame (as there is 4 in on left, on right, top and bottom).

The length of the painting is l and therefore the width is( l-3). So from the formula for area of a rectangle =l x b we deduce:

A = l(l-3)

The width of the overall painting plus frame will also be 3 inches narrower (shorter). Therefore:

270 = l(l-3)

270 = l^2 - 3l

0= l^2 - 3l - 270

0= (l+15)(l-18)

l=-15 (but l cannot equal -15)

or l = 18

It follows that the length of the painting plus frame is 18 in, the width is 15 in and as there is 4 in each side to deduct, the width of the painting is (15-8) 7in and the length is (18-8) 10 in as the frame is the same width all the way round.

**Painting: 10in by 7 in**

**Frame and painting: 18in by 15 in**