Question

Square ASDF has diagonals ( line) AD and (line) SF. Determine the length of (line) SF if (line) AD=8x-5 and (line) SF= 4x+3. Answers…SF= 24 SF =8SF=5 SF=11

Answer 1

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

`\begin{gathered} AD=8x-5 \\ SF=4x+3 \end{gathered}`

Please note that the diagonals of a square are equal. So, diagonal AD and diagonal SF are equal.

`\begin{gathered} AD=SF \\ 8x-5=4x+3 \\ 8x-4x=3+5 \\ 4x=8 \\ x=(8)/(4) \\ x=2 \end{gathered}`

Therefore, line SF is

`\begin{gathered} SF=4x+3 \\ SF=4(2)+3 \\ SF=8+3 \\ SF=11 \end{gathered}`

Hence, SF = 11