7.1.2 Ratios in Similar Polygons (continued)
In this example, two triangles are compared to determine whether they are similar. The similarity ratio is calculated. The lengths of all three sides for each rectangle are given. It is given that the triangles share one congruent angle. To determine whether the triangles are similar, calculate the ratios of lengths of each hypothesized congruent pair of sides. Two of the sides have lengths in a ratio of 4/3. The third sides have lengths in a ratio of 3/2. Because the ratios are not the same, the sides are not all proportional, and these are not similar triangles.
Example 3 Architecture Application
A scale drawing of a rectangular room is compared with the actual rectangular room in this application example. The unknown length of a side of the actual room is determined. The lengths of two sides of the drawing of the rectangular room are given. The length of one side of the actual rectangular room is given. To determine the unknown length of the side of the kitchen, set up the proportion using the ratios of the side lengths for the kitchen and the drawing. In this case, the proportion is: the length in the drawing is to the length of the kitchen ( x ) as the width in the drawing is to the width of the kitchen. Cross multiply the proportion and solve for the value of x , the length of the kitchen. The solution yields an approximate length of 7.7 feet for the length of the kitchen.
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