Trig
posted by Hellga on .
Please EXPLAIN the steps on how to solve these problems. Please provide detailed steps.
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.

The 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. 
Sorry, the diagram didn't survive the font change.

For 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.