Question

Quadrilateral RSTU is a rectangle. If U, Z, equals, x, plus, 21UZ=x+21 and Z, S, equals, 3, x, minus, 15ZS=3x−15, what is U, SUS?

Answer
Attempt 1 out of 2

Additional Solution
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U, S, equalsUS=
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Answer 1

Since Z is the intersection of the diagonals of rectangle RSTU, Z is the midpoint of diagonal US, so UZ = ZS. Set
x + 21 = 3x − 15
Solve: 21 + 15 = 3x − x ⇒ 36 = 2x ⇒ x = 18.

Then UZ = 18 + 21 = 39 and ZS = 3(18) − 15 = 39, so US = UZ + ZS = 39 + 39 = 78.