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Find the length of the third side. If necessary, write in simplest radical form.
5,
√106

Find the length of the third side. If necessary, write in simplest radical form. 5, √106-example-1
User Kyle Muir
by
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1 Answer

2 votes

Answer:

Length of third side = 9

Explanation:

Because this is a right triangle, we can find the length of the third side using the Pythagorean theorem, which uses the equation a^2 + b^2 = c^2, where

  • a and b are the lengths of the shortest sides called legs,
  • and c is the length of the longest side called the hypotenuse (always opposite the right angle).

Thus, we can plug in 5 for a and √106 for c to find b, the length of the third side:

Step 1: Plug in 5 for a and √106 for for c. Then simplify:

5^2 + b^2 = (√106)^2

25 + b^2 = 106

Step 2: Subtract 25 from both sides:

(25 + b^2 = 106) - 25

b^2 = 81

Step 3: Take the square root of both sides to find b, the length of the third side:

√(b^2) = √81

b = ± 9

  • Taking the square root of a number always gives both a positive and negative answer since squaring both a positive and negative answer yields a positive answer: Example: 4^2 = 16 and (-4)^2 = 16.

However, we can't have a negative side length so the third side is 9 units.

User BitByteDog
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