Question

How can i resolve this?​

Answer 1

`\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2 \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{100}\\ a=\stackrel{adjacent}{FP}\\ o=\stackrel{opposite}{F K} \end{cases}`

`(100)^2= (FP)^2 + (F K)^2\hspace{5em}\stackrel{\textit{since we know that FP=F K}}{FP=F K=x} \\\\\\ 100^2=x^2+x^2\implies 100^2=2x^2\implies \cfrac{100^2}{2}=x^2\implies \sqrt{\cfrac{100^2}{2}}=x \\\\\\ \cfrac{100}{√(2)}=x\implies \cfrac{100}{√(2)}\cdot \cfrac{√(2)}{√(2)}=x\implies \cfrac{100√(2)}{2}=x\implies 50√(2)=x~~ =FP=F K`