Question

question solve for a and b

Explanation:

Step1: Identify triangle type

This is a 45 - 45 - 90 right - triangle. In a 45 - 45 - 90 triangle, the two legs are equal, i.e., $a = b$.

Step2: Apply Pythagorean theorem

For a right - triangle, $a^{2}+b^{2}=c^{2}$. Since $a = b$ and $c = 5$, we have $a^{2}+a^{2}=5^{2}$, which simplifies to $2a^{2}=25$.

Step3: Solve for a

Divide both sides of $2a^{2}=25$ by 2: $a^{2}=\frac{25}{2}$. Then $a=\sqrt{\frac{25}{2}}=\frac{5}{\sqrt{2}}=\frac{5\sqrt{2}}{2}$. Since $a = b$, $b=\frac{5\sqrt{2}}{2}$.

Answer:

$a=\frac{5\sqrt{2}}{2}$, $b=\frac{5\sqrt{2}}{2}$