Question

question
solve for a and b
answer attempt 1 out of 3
a =
b =

Explanation:

Step1: Identify the triangle type

This is a 45 - 45 - 90 right - triangle. In a 45 - 45 - 90 triangle, the ratio of the sides is $a:b:h = 1:1:\sqrt{2}$, where $a$ and $b$ are the legs and $h$ is the hypotenuse.

Step2: Set up the relationship

Let the length of each leg be $x$ (so $a = b=x$), and the hypotenuse $h = 3\sqrt{2}$. According to the ratio, $h=\sqrt{2}x$.

Step3: Solve for $x$

We have the equation $3\sqrt{2}=\sqrt{2}x$. Divide both sides of the equation by $\sqrt{2}$: $\frac{3\sqrt{2}}{\sqrt{2}}=x$, so $x = 3$.

Answer:

$a = 3$
$b = 3$