Question

question solve for a and b

Explanation:

Step1: Identify the triangle type

This is a 45 - 45 - 90 right - triangle. In a 45 - 45 - 90 triangle, the legs are equal, i.e., $a = b$, and the hypotenuse $c$ is related to the legs $a$ and $b$ by the formula $c=\sqrt{2}a$.

Step2: Solve for $a$ and $b$

Given $c = 18$, and $c=\sqrt{2}a$. Then $a=\frac{c}{\sqrt{2}}$. Substitute $c = 18$ into the formula: $a=\frac{18}{\sqrt{2}}=\frac{18\sqrt{2}}{2}=9\sqrt{2}$. Since $a = b$, $b = 9\sqrt{2}$ too.

Answer:

$a = 9\sqrt{2}$
$b = 9\sqrt{2}$