Question

given a right triangle with legs a and b and hypotenuse c, find the length of side b if c = 2b, a = 12. answer: b =

Explanation:

Step1: Apply Pythagorean theorem

$a^{2}+b^{2}=c^{2}$

Step2: Substitute given values

Since $c = 2b$ and $a=12$, we have $12^{2}+b^{2}=(2b)^{2}$.

Step3: Expand and simplify

$144 + b^{2}=4b^{2}$.
Then $144=4b^{2}-b^{2}$, so $144 = 3b^{2}$.

Step4: Solve for $b^{2}$

$b^{2}=\frac{144}{3}=48$.

Step5: Solve for $b$

$b=\sqrt{48}=4\sqrt{3}$.

Answer:

$4\sqrt{3}$