A right triangle is shown below.
Find the lengths of the sides of the triangle.
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A right triangle is shown below.
Find the lengths of the sides of the triangle.
To solve this problem, we begin by using the Pythagorean theorem, as the triangle is right-angled. Let's identify the hypotenuse:
Using the Pythagorean theorem, we write:
Let's expand and simplify the equation:
Simplifying further:
Rearrange all terms to one side:
Simplifying gives:
This is a standard quadratic equation, which we can solve using factoring. By factoring, we find:
Setting each factor equal to zero gives solutions and . Since , we discard .
The valid solution is .
Now, substitute back into the expressions for the side lengths:
Therefore, the lengths of the sides of the triangle are , , and , which matches choice 4.
Therefore, the correct answer is choice 4: .
Find the value of the parameter x.
\( 2x^2-7x+5=0 \)
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