Question

find x.
10 m
6 m
x
x = \square meters
submit

Explanation:

Step1: Identify the triangle type

This is a right - triangle, so we can use the Pythagorean theorem. The Pythagorean theorem states that for a right - triangle with hypotenuse \(c\) and legs \(a\) and \(b\), \(a^{2}+b^{2}=c^{2}\). In this triangle, the hypotenuse \(c = 10\) m, one leg \(b = 6\) m, and the other leg is \(x\) (let \(a=x\)).

Step2: Rearrange the Pythagorean theorem to solve for \(x\)

We can rewrite the Pythagorean theorem as \(x^{2}=c^{2}-b^{2}\). Substitute \(c = 10\) and \(b = 6\) into the formula:
\(x^{2}=10^{2}-6^{2}\)
First, calculate \(10^{2}=100\) and \(6^{2}=36\). Then \(x^{2}=100 - 36=64\).

Step3: Solve for \(x\)

Take the square root of both sides. Since \(x\) represents the length of a side of a triangle, we take the positive square root. So \(x=\sqrt{64}=8\).

Answer:

\(x = 8\) meters