Question-219118

Question Number 219118 by Spillover last updated on 19/Apr/25

Answered by A5T last updated on 20/Apr/25

R^2 =((a/2))^2 +a^2 ⇒R=((a(√5))/2) L=R−(a/2)=((a((√5)−1))/2) ⇒(a/L)=(2/( (√5)−1))=(((√5)+1)/2)

$$\mathrm{R}^{\mathrm{2}} =\left(\frac{\mathrm{a}}{\mathrm{2}}\right)^{\mathrm{2}} +\mathrm{a}^{\mathrm{2}} \Rightarrow\mathrm{R}=\frac{\mathrm{a}\sqrt{\mathrm{5}}}{\mathrm{2}} \\ $$$$\mathrm{L}=\mathrm{R}−\frac{\mathrm{a}}{\mathrm{2}}=\frac{\mathrm{a}\left(\sqrt{\mathrm{5}}−\mathrm{1}\right)}{\mathrm{2}} \\ $$$$\Rightarrow\frac{\mathrm{a}}{\mathrm{L}}=\frac{\mathrm{2}}{\:\sqrt{\mathrm{5}}−\mathrm{1}}=\frac{\sqrt{\mathrm{5}}+\mathrm{1}}{\mathrm{2}} \\ $$

Commented by Spillover last updated on 20/Apr/25