Question

If the diagonal of the 4:3 rectangle measures 10 inches how long are its sides

Answer 1

Check the picture below.

`\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2 \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{10}\\ a=\stackrel{adjacent}{3x}\\ o=\stackrel{opposite}{4x} \end{cases} \\\\\\ (10)^2= (3x)^2 + (4x)^2\implies 100=9x^2+16x^2\implies 100=25x^2 \\\\\\ \cfrac{100}{25}=x^2\implies 4=x^2\implies √(4)=x\implies 2=x \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \stackrel{ 3(2) }{\text{\LARGE 6}}\hspace{5em}\stackrel{ 4(2) }{\text{\LARGE 8}}~\hfill`