Question

which statement about the figure must be true? select all that apply.
a. ( n = 7 )
b. ( qs = 21 )
c. ( sr = 27 )
d. ( qr = 54 )

Explanation:

Step1: Set up the equation

Since the two sides \(PQ = PR\) (marked with equal signs), by the property of isosceles triangles (the perpendicular from the vertex to the base bisects the base), we have \(QS=SR\). So, \(6n + 3=4n+11\).

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Step2: Calculate \(QS\), \(SR\) and \(QR\)

• For \(QS\): Substitute \(n = 4\) into \(QS=6n + 3\). Then \(QS=6\times4+3=24 + 3=27\).
• For \(SR\): Substitute \(n = 4\) into \(SR=4n + 11\). Then \(SR=4\times4+11=16+11=27\).
• For \(QR\): \(QR=QS + SR\). Since \(QS = 27\) and \(SR=27\), then \(QR=27+27 = 54\).

Answer:

D. \(QR = 54\)