Question

QRST is a rectangle. Find the value of x and the length of each diagonal. QS = 5x + 12 and RT = 6x – 2

Answer 1

We can draw the rectangle QRST as:

The two diagonals of a rectangle will have the same length, so we can write:

$\begin{gathered} QS=RT \\ 5x+12=6x-2 \\ 5x-6x=-2-12 \\ -x=-14 \\ x=14 \end{gathered}$

With the value of x, we can calculate the length of the diagonal:

$QS=5x+12=5\cdot14+12=70+12=82$

Answer: the lengths of the diagonals QS and RT is 82.