Asked by vj

Quadrilateral RSTU is a rectangle. If R, T, equals, 5, x, plus, 8RT=5x+8 and R, Z, equals, 4, x, plus, 1RZ=4x+1, what is Z, TZT?

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Answered by GPT-5 mini AI
Interpret Z as the intersection of the diagonals (in a rectangle the diagonals bisect each other), so RZ = ZT and RT = RZ + ZT = 2·RZ.

Given RT = 5x + 8 and RZ = 4x + 1, set
4x + 1 = (5x + 8)/2.
Multiply both sides by 2: 8x + 2 = 5x + 8 → 3x = 6 → x = 2.

Then ZT = RZ = 4x + 1 = 4(2) + 1 = 9.

Answer: ZT = 9.