Solving problems with Ratio |
The length of sides of a triangle (in centimeters) is represented by the ratio 2:3:4. If the perimeter of the triangle is 45cm, find the length of each side? Solution: First we add up all the numbers in the ratio (2 + 3 + 4 = 9) Now, the best way to understand what follows is to imagine a triangle with the sides of 2cm, 3cm and 4cm (perimeter of 9cm) being blown-up or enlarged to a size where the perimeter becomes 45cm. In other words, what we are trying to find is the number of times that the earlier triangle (with perimeter of 9cm) must be enlarged to produce the later triangle. To get that we take the perimeter of 45cm and divide it by the perimeter of 9cm:
This means that each of the sides will be enlarged 5 times the gives size. Thus, the sides will be: 2cm x 5 : 3cm x 5: 4cm x 5 respectively giving us a triangle with, 10cm, 15cm and 20cm sides. If you want to prove that your answer is right, you can add up these numbers and you should be able to get 45cm. Ratio ad the money problemThe concept of ratio can also be used to solve issues with money. Consider the following example: Jen has 3 times as much money as Angie. If Jen gives 50 cents of her money to Angie, they will both have the same amounts. How much money did each have before Jen gave Angie 50 cents. Solution What do we know? : The ratio of Jen to Angie amounts is 3:1 The whole situation can then be presented in the form of an equation as follows: Let the unknown amount be x cents, 3x - 50 = x + 50 3x - x = 50 + 50 2x = 100 cents x = 50 cents This means that Jen had 3(50 cents) = 150 cents and Angie had 1(50 cents) = 50 cents. After Jen gave 50 cents of her money to Angie, she was left with 100 cents. After Angie had acquired another 50 cents, she now has 100 cents, which is the same as Jen's. |
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