The area of a frame is equal to 120in^2.it surrounds a 4in x 6in photo.the frame is of uniform width.how wide is the frame ?
the 4x6 photo has area 24 in^2
So, the frame has area 120-24 = 96 in^2
If the frame has width x, then its area is
2(4x) along the ends
+2(6x) along the sides
+4x^2 on the corners
so,
4x^2 + 8x + 12x = 96
x^2 + 5x - 24 = 0
x = 3
So, the frame is 3in wide
check:
total dimensions are 10x12, so area = 120
To find the width of the frame, we can subtract the area of the photo from the area of the frame.
First, let's calculate the area of the photo:
Area of the photo = length of the photo x width of the photo
= 4in x 6in
= 24in^2
Now, subtract the area of the photo from the total area of the frame to get the area of the frame:
Area of the frame = Total area – Area of the photo
= 120in^2 – 24in^2
= 96in^2
Since the frame has a uniform width, all sides of the frame will have the same width. Let's assume the width of the frame to be 'x' inches.
The area of the frame can be calculated as:
Area of the frame = (length of the photo + 2 * width of the frame) * (width of the photo + 2 * width of the frame)
Plugging in the values we know:
96in^2 = (4in + 2x)(6in + 2x)
Now, we can solve this quadratic equation for 'x':
96in^2 = (4in + 2x)(6in + 2x)
96in^2 = 24in^2 + 16in * x + 12in * x + 4x^2
0 = 20in^2 + 28in * x + 4x^2
To solve this quadratic equation, we can either factorize it or use the quadratic formula.
By factoring, we can write it as:
0 = 4(x^2 + 7in * x + 5in^2)
Setting each factor to zero, we get:
x^2 + 7in * x + 5in^2 = 0
Now we can solve this quadratic equation.