Question

quadrilateral cdef is a rhombus. what is cf?
f
e
2b+78
c
d
b+89
cf =
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Explanation:

Step1: Recall rhombus side property

In a rhombus, all sides are equal. So \( CF = DE \) and \( CD = DE \), thus \( CD = CF \). So \( b + 89=2b + 78 \).

Step2: Solve for \( b \)

Subtract \( b \) and 78 from both sides: \( b + 89 - b - 78=2b + 78 - b - 78 \), which simplifies to \( 11 = b \).

Step3: Find \( CF \)

Since \( CF = CD \) and \( CD = b + 89 \), substitute \( b = 11 \): \( CF = 11 + 89 = 100 \).

Answer:

100