Arectangular canvas picture measures 10 inches by 8 inches. the canvas is mounted inside a frame of uniform width, increasing the total area covered by both canvas and frame to 120 square inches. find the uniform width of the frame.

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.

you need to show the graph

step-by-step explanation:

b

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