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Similar Figures - Calculate Dimensions Using Proportions

by Malaika
(Memphis, TN)











































Similar Rectangles

Pat's school photo package includes one large photo and several smaller photos. The large photo is similar to a photo measuring 2 in. × 1.5 in. If the height of the large photo is 10 in., what is its width?

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Jan 04, 2013
Similar Rectangles
by: Staff


Answer

Part I


A diagram of the problem is shown below:

Math – Similar Rectangles – Scale Factor






Since the large photo and the small photo are similar geometric shapes, you can solve for one dimension (either width or height) of either figure as long as you know the scale factor.

The scale factor is a ratio which can be computed from the information given in the problem statement.

The ratio is the length of one of the sides of either photo to the length of the corresponding side of the other photo.

Scale factor = (width of large photo) / (width of small photo)

Scale factor = (height of large photo) / (height of small photo)


Regardless of whether the scale factor is computed based on the height of the two photos or the width of the two photos, the numerical value of the scale factor will be the same.

The dimensions given in the problem statement are:

Large photo


           Width of large photo = unknown

           Height of large photo = 10 inches

Small photo

           Width of small photo = 1.5 inches

           Height of small photo = 2 inches



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Jan 04, 2013
Similar Rectangles
by: Staff


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Part II

The scale factor can be computed using the height of the large photo and the height of the small photo:

Scale factor = (height of large photo) / (height of small photo)

Scale factor = (10 inches) / (2 inches)

Scale factor = 5



As already noted, the scale factor is the same (because the two geometric shapes are “similar”) regardless of which dimension is used to calculate it:

Scale factor = (height of large photo) / (height of small photo) = 5

Scale factor = (width of large photo) / (width of small photo) = 5



To find the width of the large photo, substitute the known values in the following equation:


(width of large photo) / (width of small photo) = scale factor

(width of large photo) / (width of small photo) = 5

(width of large photo) / (1.5 inches) = 5


Now solve for the width of the large photo:

[(width of large photo) / (1.5 inches)] * (1.5 inches) = 5 * (1.5 inches)

(width of large photo) * [(1.5 inches) / (1.5 inches)] = 5 * (1.5 inches)

(width of large photo) * 1 = 5 * (1.5 inches)

(width of large photo) = 5 * (1.5 inches)

(width of large photo) = 7.5 inches




Final Answer:

width of large photo = 7.5 inches





Math – Similar Rectangles – Width of large photo









Thanks for writing.

Staff
www.solving-math-problems.com



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