Triangle Problem Solving

The perimeter of the triangle is the sum of the measures of its sides. Problem 3 Find the missed side of the triangle, if the first side is 7 cm long, the second side is 2 cm shorter and the perimeter of the triangle is 16 cm.Therefore, it is equal to 8 cm 12 cm 10 cm = 30 cm. Solution The second side is 7 cm - 2 cm = 5 cm long in accordance with the problem condition.

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Once you've learned about trigonometric ratios (and their inverses), you can solve triangles.

Naturally, many of these triangles will be presented in the context of word problems.

Problem 1 Find the perimeter of the triangle with the sides of 8 cm, 5 cm and 9 cm long.

Solution The perimeter of the triangle is the sum of the measures of its sides. Problem 2 Find the perimeter of the triangle, if the first side is of 8 cm long, the second side is in 4 cm longer, and the third side measure is half of the sum of that of the first and the second sides.

Find the measures of the triangle sides, if the perimeter of the triangle is 40 cm.

Solution Let x be the first side measure (in centimeters).Simplify this equation step by step and solve it: x x 7 x 3 = 40, 3x 10 = 40, 3x = 40 - 10, 3x = 30, x = 10. Hence, the second side is 10 cm 7 cm = 17 cm long, and the third side is 17 cm - 4 cm = 13 cm long in accordance with the problem condition.You can check that the sum of the side measures is equal to the given value of the perimeter: 10 cm 17 cm 13 cm = 40 cm. The sides of the triangle are 10 cm, 17 cm and 13 cm long.Alternatively, you can consider the solution using the reduction to the some kind of a linear equation.The examples below show how each of these approaches works.A good first step, after reading the entire exercise, is to draw a right triangle and try to figure out how to label it.Once you've got a helpful diagram, the math is usually pretty straightforward.Since the perimeter of the triangle is 16 cm and the two sides measures are 7 cm and 5 cm, the missed third side length is 16 cm - (7 cm 5 cm) = 16 - 12 cm = 4 cm. The length of the missed third side of the triangle is 4 cm.Problem 4 In a triangle, the second side is in 7 cm longer than the first one and the third side is in 4 cm shorter than the second one.Note: Unless you are told to give your answer in decimal form, or to round, or in some other way not to give an "exact" answer, you should probably assume that the "exact" form is what they're wanting.For instance, if they hadn't told me to round in the exercise above, my value for the height should have been the value with the radical. That width will be twice the base of one of the right triangles.

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