Question

Please answer quick!! 15 points!!! In a right triangle the length of a hypotenuse is c and the length of one leg is a, and the length of the other leg is b, what is the value of b, if a=3b, c=2√10

Answer 1

b = 2

Explanation:

`\text{Use the Pythagorean theorem:}\\\\leg^2+leg^2=hypotenuse^2\\\\\text{We have}\\\\leg=a=3b\\leg=b\\hypotenuse=2√(10)\\\\\text{Substitute}\\\\(3b)^2+b^2=(2√(10))\qquad\text{use}\ (ab)^n=a^nb^n\\\\3^2b^2+b^2=2^2(√(10))^2\qquad\text{use}\ (√(a))^2=a\ \text{for}\ a\geq0\\\\9b^2+b^2=4(10)\qquad\text{combine like terms}\\\\10b^2=40\qquad\text{divide both sides by 10}\\\\b^2=4\to b=\sqrt4\\\\b=2`