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?
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.
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.
To find the width of the frame, we need to subtract the area of the picture from the total area covered by the frame and picture.
Given:
Length of the picture = 7 inches
Width of the picture = 7 inches
Area of the picture = Length × Width = 7 inches × 7 inches = 49 square inches
Total area covered by the frame and picture = 32 + 49 = 81 square inches
Let's assume the width of the frame as "w" inches.
So, the length of the frame will be (7 + 2w) inches, and the width of the frame will be (7 + 2w) inches.
Area covered by the frame and picture = (length of the frame) × (width of the frame)
81 = (7 + 2w) × (7 + 2w)
81 = 49 + 14w + 14w + 4w^2
81 = 49 + 28w + 4w^2
4w^2 + 28w + 49 - 81 = 0
4w^2 + 28w - 32 = 0
Let's solve this quadratic equation by factoring or using the quadratic formula.
Factoring the equation: (2w - 2)(2w + 16) = 0
Setting each factor equal to zero:
2w - 2 = 0 or 2w + 16 = 0
Solving for w:
2w = 2 or 2w = -16
w = 1 or w = -8 (ignoring the negative value)
The width of the frame cannot be negative, so we will take w = 1 inch.
Therefore, the width of the frame is 1 inch.
To find the width of the frame, we need to subtract the area of the picture from the total area of the frame.
First, let's find the area of the picture. The picture measures 7 inches by 7 inches, so the area of the picture is calculated by multiplying the length and width together:
Area of the picture = Length of the picture × Width of the picture
= 7 inches × 7 inches
= 49 square inches
Next, we subtract the area of the picture from the total area of the frame:
Width of the frame = Total area of the frame - Area of the picture
The total area of the frame is given as 32 square inches. So, let's substitute the values into the equation:
Width of the frame = 32 square inches - 49 square inches
= -17 square inches
However, we cannot have a negative width for the frame, so there seems to be a logical error or missing information in the problem statement. Please double-check the values provided to ensure accuracy.