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

Sagot :

We can draw the rectangle QRST as:

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

[tex]\begin{gathered} QS=RT \\ 5x+12=6x-2 \\ 5x-6x=-2-12 \\ -x=-14 \\ x=14 \end{gathered}[/tex]

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

[tex]QS=5x+12=5\cdot14+12=70+12=82[/tex]

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

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