Given: Square ASDF has diagonals ( line) AD and (line) SF
To Determine: The length of (line) SF if (line) AD=8x-5 and (line) SF= 4x+3
Solution:
The diagram below represents the given square
Given that
[tex]\begin{gathered} AD=8x-5 \\ SF=4x+3 \end{gathered}[/tex]Please note that the diagonals of a square are equal. So, diagonal AD and diagonal SF are equal.
[tex]\begin{gathered} AD=SF \\ 8x-5=4x+3 \\ 8x-4x=3+5 \\ 4x=8 \\ x=\frac{8}{4} \\ x=2 \end{gathered}[/tex]Therefore, line SF is
[tex]\begin{gathered} SF=4x+3 \\ SF=4(2)+3 \\ SF=8+3 \\ SF=11 \end{gathered}[/tex]Hence, SF = 11
