Does anyone know this?
1 answer:
You might be interested in
Answer:
The uniform width of the frame is 1 inch
Step-by-step explanation:
Hi there!
Please see the attached figure for a graphical description of the problem.
The area of a rectangle is calculated multiplying the length times the width.
In this case, the length of the rectangle (canvas + frame) is 10 inches + 2x (see figure), while the widht is 8 inches + 2x. Then:
area of the rectangle = (8 + 2x) · (10 + 2x) = 120
Now we have our equation. If we solve it for x, we will obtain the uniform width of the frame:
120 = (8 + 2x) · (10 + 2x)
Apply distributive property:
120 = 80 + 16x + 20x + 4x²
Subtract 120 to both sides of the equation:
0 = -120 + 80 + 16x + 20x + 4x²
0 = -40 + 36x + 4x²
Solve the quadratic equation using the quadratic formula:
a = 4
b = 36
c = -40
x = [-b ± √(b² - 4ac)]/2a
x = 1
(the second solution is negative and therefore discarded).
Then, the uniform width of the frame is 1 inch.
