Respuesta :
Recall the property of a rectangle that its diagonals are congruent, therefore
[tex]\begin{gathered} QS=RT \\ \\ \text{Substitute the following given and solve for }x \\ QS=20x-3 \\ RT=16x+5 \\ \\ QS=RT \\ 20x-3=16x+5 \\ 20x-16x=5+3 \\ 4x=8 \\ \frac{4x}{4}=\frac{8}{4} \\ x=2 \end{gathered}[/tex]Now that we have x = 2 as our solution, substitute it to any of the equation for the diagonals. We will use QS (using RT works just as well)
[tex]\begin{gathered} QS=20x-3 \\ QS=20(2)-3 \\ QS=40-3 \\ QS=37 \\ \\ \text{Since }QS\text{ is equal to 37, it follows that }RS\text{ is also equal to 37} \end{gathered}[/tex]Therefore, the length of the diagonals is 37 units.
