Question

what is the measure of side b?

Explanation:

Step1: Identify the triangle type

Assume it's a right - isosceles triangle (since no other angle information is given and we often deal with special right - triangles in such cases). In a right - isosceles triangle, the two legs are of equal length and if the hypotenuse is $c$ and the legs are $a$ and $b$ (where $a = b$), by the Pythagorean theorem $c^{2}=a^{2}+b^{2}$. Since $a = b$, we have $c^{2}=2b^{2}$.

Step2: Given $c = 10$

If $c = 10$, then $10^{2}=2b^{2}$, so $100 = 2b^{2}$.

Step3: Solve for $b$

First, divide both sides of the equation $100 = 2b^{2}$ by 2: $\frac{100}{2}=b^{2}$, which gives $b^{2}=50$. Then take the square - root of both sides: $b=\sqrt{50}=\sqrt{25\times2}=5\sqrt{2}$.

Answer:

$5\sqrt{2}$