Question

the two shorter legs of a right triangle are 3 cm and 8 cm in length. which equation can be used to find x, the length of the hypotenuse of the right triangle?
$8^{2}-3^{2}=x$
$3^{2}+8^{2}=x$
$3 + 8 = x$
$(3 + 8)^{2}=x$

Explanation:

Step1: Recall the Pythagorean theorem

For a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), the formula is \(a^{2}+b^{2}=c^{2}\). Here \(a = 3\), \(b = 8\) and \(c=x\).

Step2: Substitute the values into the formula

Substituting \(a = 3\) and \(b = 8\) into \(a^{2}+b^{2}=c^{2}\), we get \(3^{2}+8^{2}=x^{2}\). But if we consider the equations given (assuming a mis - representation of the Pythagorean theorem in the options where they might have missed the square on \(x\) but among the given options, the structure based on \(a^{2}+b^{2}\) is what we look for).

Answer:

The equation \(3^{2}+8^{2}=x\) (assuming a square on \(x\) is missed in the problem's options representation, and among the given options, this is the one following the \(a^{2}+b^{2}\) structure of the Pythagorean theorem) is the most appropriate. So the answer is \(3^{2}+8^{2}=x\) (if we consider the form based on the sum of squares of legs related to hypotenuse, even with a possible typo in the problem's options regarding the square on \(x\)).