Exercise 110 Page 364

a If we scale down the triangle as much as we can and get two sides that match two sides in either a 3-4-5 triangle or a 5-12-13 triangle, we know the triangle is a Pythagorean Triple. In the given triangle the hypotenuse is 15 units and one leg is 12 units, so we can scale down the triangle by dividing the sides by 3.

Now we know that the given triangle is a dilated version of a 3-4-5 triangle. The unknown side in the given triangle corresponds to the leg in a 3-4-5 triangle that has a length of 3. With this information we can write and solve an equation for x. x/3= 3 ⇔ x=9 units

b Like in Part A we will scale down the triangle as much as possible to investigate what type of Pythagorean Triple it might be. Both legs are multiples of 2, which means we can divide both sides by this factor.

As we can see, the given triangle is a dilated version of a 5-12-13 triangle. The unknown side in the given triangle corresponds to the hypotenuse in a 5-12-13 triangle that has a length of 13. With this information we can write and solve an equation for x. x/2= 13 ⇔ x=26 units

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Exercise 110 Page 364

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