Question

A square has a one-inch frame. If the area of the frame alone is 48 square inches, what is the area of the picture?

Answer 1

121 sq. in

Explanation:

area of the frame = 48 square inches

if
`x` is the side length of the square, then (
`x` + 2) is the side length of the square after the frame has been added.

the area of the picture + the frame is:

(
`x` + 2) (
`x` + 2)

the area of just the frame is given by (
`x` + 2) (
`x` + 2) -
`x` x
`x`:

(
`x` + 2) (
`x` + 2) -
`x` x
`x` =48

`x`²+
`x` x 2 + 2 x
`x` + 2 x 2-
`x`² = 48

`x`² + 2
`x` + 2
`x` + 4-
`x`² = 48

4
`x` + 4 = 48

then subtract 4 from both sides:

4x = 44

and divide both sides by 4:

x = 11

the area of the square is 11 (11) = 121.

i think this is correct?

hope this helps :))