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?

8² - 3² = x

3² + 8² = x

3 + 8 = x

(3 + 8)² = x

Explanation:

Step1: Recall Pythagorean theorem

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

Step2: Substitute values

Substitute \(a = 3\) and \(b = 8\) into the Pythagorean theorem. 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 maybe they forgot the square on \(x\) but among the given options, the structure based on \(a^{2}+b^{2}=c^{2}\) is \(3^{2}+8^{2}=x\) (if we assume the options have a typo in squaring \(x\)). The other options:

• For \(8^{2}-3^{2}=x\), this is not the Pythagorean formula. The Pythagorean formula is \(a^{2}+b^{2}=c^{2}\) not \(a^{2}-b^{2}=c^{2}\).
• For \(3 + 8=x\), this is wrong because in a right - triangle, the sum of the lengths of the two legs is not equal to the length of the hypotenuse.
• For \((3 + 8)^{2}=x\), \((3 + 8)^{2}=3^{2}+2\times3\times8 + 8^{2}

eq3^{2}+8^{2}\)

Answer:

\(3^{2}+8^{2}=x\) (assuming a typo in the problem's options regarding the square of \(x\), as the correct formula is \(3^{2}+8^{2}=x^{2}\), but among the given options, the one that follows the structure of \(a^{2}+b^{2}=c^{2}\) (ignoring the square on \(x\) in the options) is \(3^{2}+8^{2}=x\))