Question

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

The Pythagorean theorem for a right - triangle is $a^{2}+b^{2}=c^{2}$. Since $a = b$ and $c = 14$, we have $a^{2}+a^{2}=14^{2}$, which simplifies to $2a^{2}=196$.

Step3: Solve for a

Divide both sides of $2a^{2}=196$ by 2: $a^{2}=\frac{196}{2}=98$. Then take the square root of both sides: $a=\sqrt{98}=\sqrt{49\times2}=7\sqrt{2}$. Since $b = a$, $b = 7\sqrt{2}$ as well.

Answer:

$a = 7\sqrt{2}$
$b = 7\sqrt{2}$