find the value of x in the isosceles triangle shown below. choose 1 answer.

Explanation:

Step1: Apply Pythagorean theorem

Let the isosceles triangle be divided into two right - triangles by the perpendicular from the vertex to the base. In a right - triangle, if the hypotenuse is $c = \sqrt{74}$ and one side is $b = 7$, and the other side is $a=x$. According to the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, so $x^{2}+7^{2}=(\sqrt{74})^{2}$.

Step2: Simplify the equation

We know that $(\sqrt{74})^{2}=74$ and $7^{2} = 49$. The equation $x^{2}+49 = 74$.

Step3: Solve for $x$

Subtract 49 from both sides of the equation: $x^{2}=74 - 49$, so $x^{2}=25$. Then take the square - root of both sides. Since $x$ represents the length of a side of a triangle, we take the positive square - root, and $x = 5$.

Answer:

$5$