7*7=49=area of picture
32+49=81=area of frame and picture
since the width of the frame is uniform, the frame is also a square just like the picture.
so sqrt{81}=9
the frame is 9 by 9
9-7=2
the frame is 2 inches wide.
A picture that measures 7 inches by 7 inches is being framed. The area of the frame is 32 square inches. What is the width of the frame?
2 answers
If the square is 7 by 7 inches then it equals 49 inches.
The frame is also a square.
So, the frame would be outside the 49 inch square.
Therefore, the 7 by 7 inche square will be increased by an unknown number, x.
so that means that one side of the frame would be 7+2x.
The area of a square is s^2.
So, the area of the whole thing is (7+2x)^2
Now, that is the area of the whole thing.
So, then you must subtract the area of the square away from the area of it all. To get 32 inches. which, is the area of the frame.
There fore, the equation to oslve this problem would be
(7+2x)^2-49=32
Add 49 to both sides.
(7+2x)^2=81
Square root both sides.
7+2x=9
Subtract 7
2x=2
Divide.
x=1
the width is one.
The frame is also a square.
So, the frame would be outside the 49 inch square.
Therefore, the 7 by 7 inche square will be increased by an unknown number, x.
so that means that one side of the frame would be 7+2x.
The area of a square is s^2.
So, the area of the whole thing is (7+2x)^2
Now, that is the area of the whole thing.
So, then you must subtract the area of the square away from the area of it all. To get 32 inches. which, is the area of the frame.
There fore, the equation to oslve this problem would be
(7+2x)^2-49=32
Add 49 to both sides.
(7+2x)^2=81
Square root both sides.
7+2x=9
Subtract 7
2x=2
Divide.
x=1
the width is one.