Word Problem: photo 4" longer than wide, 3" border, 165sq in

Quadratic equations and inequalities, variation equations, function notation, systems of equations, etc.
bontrager
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Word Problem: photo 4" longer than wide, 3" border, 165sq in

Postby bontrager » Mon Apr 20, 2009 12:57 am

If a photo is 4 inches longer than it is wide. A 3-inch border is placed around the photo making the total area of the photo and border 165 square inches. What are the dimensions of the photo?

I'm having trouble with this word problem, if anyone can help me out it would be appreciated.

Thanks.

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stapel_eliz
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Postby stapel_eliz » Mon Apr 20, 2009 11:41 am

bontrager wrote:If a photo is 4 inches longer than it is wide. A 3-inch border is placed around the photo making the total area of the photo and border 165 square inches. What are the dimensions of the photo?

Draw a picture of the situation, consisting of two nested triangles.

Label the width of the picture as "w".

Create an expression for the length, being "(the width) plus (four more)". Label the drawing with this expression.

Label the distances between the rectangles with "3", being the width of the border.

Working from what you can see, create expressions for the width and length of the outer rectangle. (This will involve adding the values for the inner rectangle and the border distances.)

Using the expressions you just created for the length and width of the total area, along with the formula for the area A of a rectangle with a given length and width and the "area" value they gave you, create an equation representing the area of the total area. (You should end up with something like "165 = (w + 6)(w + 10)".)

Solve this equation for the value of "w".

Back-solve for the required values.

If you get stuck, please reply showing how far you have gotten. Thank you! :D


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