Question

2.1 score: 12/14 answered: 12/14 question 13 0/1 pt 3 99 details find the remaining sides of a 45° - 45° - 90° triangle if the longest side is 20. answer exactly. both shorter sides:

Explanation:

Step1: Recall side - ratio property

In a 45° - 45° - 90° triangle, if the length of the hypotenuse (the longest side) is $c$ and the length of each of the two equal shorter sides is $a$, then $c = a\sqrt{2}$.

Step2: Solve for $a$

Given $c = 20$, we have $20=a\sqrt{2}$. Solving for $a$, we get $a=\frac{20}{\sqrt{2}}$. Rationalize the denominator: $a=\frac{20\sqrt{2}}{2}=10\sqrt{2}$.

Answer:

$10\sqrt{2}$