Problem 3 Applying Area Ratios

Agriculture During the summer, a group of high school students cultivated a plot of city land and harvested 13 bushels of vegetables that they donated to a food pantry. Next summer, the city will let them use a larger, similar plot of land. In the new plot, each dimension is 2.5 times the corresponding dimension of the original plot. How many bushels can the students expect to harvest next year?

The ratio of the dimensions is 2.5 : 1. So, the ratio of the areas is ( 2 . 5 ) 2 : 1 2 , open 2 . 5 , close squared , colon . 1 squared , comma  or 6.25 : 1. With 6.25 times as much land next year, the students can expect to harvest 6.25(13), or about 81, bushels.

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3. 1. The scale factor of the dimensions of two similar pieces of window glass is 3 : 5. The smaller piece costs $ 2 . 50 . dollars 2 . 50 .  How much should the larger piece cost?
   2. Reasoning In Problem 3, why is it important that each dimension is 2.5 times the corresponding dimension of the original plot? Explain.

Problem 4 Finding Perimeter Ratios

The triangles below are similar. What is the scale factor? What is the ratio of their perimeters?

Area = 50   cm 2 equals 50 . , cm squared

Area = 98   cm 2 equals 98 . , cm squared

a 2 b 2 = 50 98 Use  a 2 : b 2 for the ratio of the areas. a 2 b 2 = 25 49 Simplify. a b = 5 7 Take the positive square root of each side. table with 3 rows and 3 columns , row1 column 1 , fraction eh squared , over b squared end fraction , column 2 equals , 50 over 98 , column 3 cap use , eh squared , colon , b squared . for the ratio of the areas. , row2 column 1 , fraction eh squared , over b squared end fraction , column 2 equals , 25 over 49 , column 3 cap simplify. , row3 column 1 , eh over b , column 2 equals , 5 sevenths , column 3 cap take the positive square root of each side. , end table

The ratio of the perimeters equals the scale factor 5 : 7.

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4. The areas of two similar rectangles are 1875   ft 2 1875 , , ft squared  and 135   ft 2 . 135 , ft squared , .  What is the ratio of their perimeters?