Question

what is the length of side x? image of a right triangle with one leg 3, another leg 4, and hypotenuse x

Explanation:

Step1: Identify the triangle type

The triangle is a right - triangle (has a right - angle mark). For a right - triangle, we can use the Pythagorean theorem, which states that for a right - triangle with legs of lengths \(a\) and \(b\) and hypotenuse of length \(c\), \(a^{2}+b^{2}=c^{2}\). Here, the legs are of lengths \(a = 3\) and \(b = 4\), and the hypotenuse is \(x\).

Step2: Apply the Pythagorean theorem

Substitute \(a = 3\) and \(b = 4\) into the formula \(a^{2}+b^{2}=c^{2}\) (where \(c=x\)). So we have \(3^{2}+4^{2}=x^{2}\). Calculate \(3^{2}=9\) and \(4^{2}=16\). Then \(9 + 16=x^{2}\), which simplifies to \(25=x^{2}\).

Step3: Solve for \(x\)

Take the square root of both sides. Since \(x\) represents the length of a side, we take the positive square root. So \(x=\sqrt{25}=5\).

Answer:

The length of side \(x\) is \(5\).