Question

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The lengths of two sides of a right triangle are 5 inches and 8 inches. What is the difference between the two possible lengths of the third side of the triangle? Round your answer to the nearest tenth.

...___inches???

Answer 1

First, you need to determine the possible side lengths of your third side. Here, your third side can be your hypotenuse or another side length. If it is your hypotenuse, it will be equal to sqrt(8^2+5^2)=sqrt(64+25)=sqrt(89). If it is your side length, it will be equal to sqrt(8^2-5^2)=sqrt(64-25)=sqrt(39). You can find the difference by subtracting these from each other in a calculator, making your difference equal to sqrt(89)-sqrt(39)≈3.2 inches.