SOLUTION: The length of a picture frame is 3 in. greater than the width. The perimiter is less than 52in. Describe the dimentions of the frame.

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Question 218757: The length of a picture frame is 3 in. greater than the width. The perimiter is less than 52in. Describe the dimentions of the frame.
Found 2 solutions by drj, MathTherapy:
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
The length of a picture frame is 3 in. greater than the width. The perimeter is less than 52in. Describe the dimensions of the frame.

Step 1. Let w be the width.

Step 2. Let w+3 be the length.

Step 3. Perimeter P means adding up all four sides of the triangle. That is, P=w%2Bw%2Bw%2B3%2Bw%2B3=4w%2B6=52

Step 4. Solving yields the following steps

4w%2B6=52

Subtract 6 to both sides of the equation

4w%2B6-6=52-6

4w=46

Divide 4 to both sides of the equation

{{4w/4=46/4}}}

w=23%2F2 and w%2B3=29%2F3%7D%7D%0D%0A%0D%0A%0D%0ACheck+P=4w%2B6=4%2A23%2F2%2B6=52 which is a true statement

Step 5. ANSWER: The width is 23%2F2 in. and length is 29%2F2 in.

I hope the above steps and explanation were helpful.

For Step-By-Step videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry please visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Also, good luck in your studies and contact me at john@e-liteworks.com for your future math needs.

Respectfully,
Dr J

http://www.FreedomUniversity.TV

Answer by MathTherapy(10549) About Me  (Show Source):
You can put this solution on YOUR website!
The length of a picture frame is 3 in. greater than the width. The perimiter is less than 52in. Describe the dimentions of the frame.

Let the width of the frame be W

Since its length is 3 inches greater than its width, then its length = W + 3

Since the perimeter is less than 52 inches, then we'll have:

2(W) + 2(W + 3) < 52

2W + 4W + 6 < 52

6W + 6 < 52

6W < 46

W <46%2F6 or <23%2F2, or <highlight_green%2811.5%29

Since width < 11.5 inches, and length is 3 more then width, then length < (11.5 + 3), or < highlight_green%2814.5%29

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Check
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Since width, or W < 11.5, and since length, or L < 14.5, then let width, or W = 11, and length, or L = 14

2W + 2L < Perimeter

2(11) + 2(14) < 52

22 + 28 < 52

50 < 52 (TRUE)