Question

RENT is a rectangle. Its diagonals meet at O. Find x, if OR = 2x + 4 and OT = 3x + 1.

Answer 1

${\displaystyle \overline{\text{OT}} \text{is half of the diagonal} \overline{\text{TE}}}$.

${\displaystyle \overline{\text{OR}} \text{is half of the diagonal} \overline{\text{RN}}}$.

by the property of Diagonals of a Rectangle Are of Equal Length.

So, their halves are also equal.

Therefore,

3x + 1 = 2x + 4

3x - 2x = 4 - 1

x = 3.