Answer:
Q1. Yes
Q2. b = 12/5
Step-by-step explanation:
[tex]\text{We have}\ a=7,\ b=24,\ c=25.\\\\\text{Substitute to}\ a^2+b^2=c^2:\\\\L_s=7^2+24^2=49+576=625\\\\R_s=25^2=625\\\\L_s=R_s\\\\\boxed{YES}[/tex]
[tex]\text{Use the Pythagorean theorem.}\\\\a^2+b^2=c^2\\\\a=1,\ c=\dfrac{13}{5}\\\\\text{Substitute:}\\\\1^2+b^2=\left(\dfrac{13}{5}\right)^2\\\\1+b^2=\dfrac{169}{25}\qquad\text{subtract 1 from both sides}\\\\b^2=\dfrac{169}{25}-1\\\\b^2=\dfrac{169}{25}-\dfrac{25}{25}\\\\b^2=\dfrac{144}{25}\to b=\sqrt{\dfrac{144}{25}}\\\\b=\dfrac{\sqrt{144}}{\sqrt{25}}\\\\b=\dfrac{12}{5}[/tex]
