Question 297609: Use the Pythagorean theorem to find the length of the unknown side of the triangle.
Write the answer as a radical in simplified form.
Square root of 17 is one side.
Square root of 5 is the second side.
And x is the third side.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! Pythagorean Theorem is c^2 = a^2 + b^2
c is the hypotenuse and a and b are the legs of the right triangle.
The hypotenuse is always bigger than either of the 2 legs.
You are given that one side of the triangle is equal to sqrt(17).
You are also given that the second side of the triangle is equal to sqrt(5).
sqrt(5) cannot be the hypotenuse of the right triangle.
sqrt(17) could.
sqrt(x) could also, since you do not know what size that is.
Assuming that x is the hypotenuse of the triangle, then the Pythagorean formula would be:
x^2 = 17 + 5
c^2 = x^2
a^2 = 17
b^2 = 5
Simplify to get:
x^2 = 23
That would make x = sqrt(23).
Assuming that 17 is the hypotenuse of the triangle, then the Pythagorean formula would be:
17 = 5 + x^2
c^2 = 17
a^2 = 5
b^2 = x^2
Subtract 5 from both sides of that equation to get:
x^2 = 17 - 5
Combine like terms to get:
x^2 = 12
That would make x = sqrt(12).
Either answer would be correct if it was not specified which side was which.
In a right triangle, the Pythagorean Formula holds:
c^2 = a^2 + b^2
With our first triangle, this becomes:
5 + 17 = 23
With our second triangle, this becomes:
5 + 12 = 17
One of these will be your correct answer once you determine which side was supposed to be 5 and which side was supposed to be 17.
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