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December 17, 2014

December 17, 2014

Posted by **Hellga** on Thursday, January 10, 2008 at 11:24pm.

A rectangle picture is 12 by 16 inches. If a frame of uniform width contains an area of 165 square inches, what is the width of the frame?

The length of a rectangular garden is 6 feet more than its width. A walkway is 3 feet wide surrounds the outside of the garen. The total area of the walkway is 288 square feet. Find the dimensions of the garden.

- Trig -
**Quidditch**, Friday, January 11, 2008 at 12:18amThe first problem:

Sketch this problem to make it easier to visualize. There is a rectangular frame with the inside dimensions of 12 * 16 inches. The frame has a width of W. You need to divide the frame into pieces and then write an equation for those pieces to equal 165 in^2. One approach would be to extend the lines of the picture to form 4 rectangles of the frame along the edges and 4 squares at the corners.

W

-------------------------

| | | | W

-------------------------

| | | |

| | 12 | |

| | | |

| | 16 | |

-------------------------

| | | | W

-------------------------

W

There are 2 rectangles that are W * 16.

There are 2 rectangles that are W * 12.

There are 4 corner squares that are W * W.

Add these 8 items and set the total to 165. Then solve for W. You will need to use the quadratic formula.

- Trig -
**Quidditch**, Friday, January 11, 2008 at 12:20amSorry, the diagram didn't survive the font change.

- Trig -
**drwls**, Friday, January 11, 2008 at 12:23amFor the rectangle problem, let w be the frame width. 165 in^2 is considered to be the frame area, not including the picture hole in the middle.

165 + (12*16) = (12+2w)(16+2w)

= 192 + 56w + 4w^2

4w^2 + 56w -165 = 0

(2w -5)(2w+33) = 0

w = 5/2 inch (ignore the negative root)

Use a similar approach for the second problem. Someone will be glad to critique your work.

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