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

Answer:

121 sq. in

Step-by-step 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 :))