Question

Find the lengths of the diagonals of rectangle QRST when QS = 20x – 3 and RT = 16x + 5.a. 37b. 74c. 18.5d. 95.9

Answer 1

Recall the property of a rectangle that its diagonals are congruent, therefore

`\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 \\ (4x)/(4)=(8)/(4) \\ x=2 \end{gathered}`

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)

`\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}`

Therefore, the length of the diagonals is 37 units.