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Suppose that quadrilateral PQRS has four congruent sides and satisfies PQ = PR. What is the value of \(\frac{QS}{PR}\)?
A. \(\frac{1}{2}\)
B. 1
C. \(\frac{\sqrt{3}}{2}\)
D. \(\sqrt{2}\)
E. \(\sqrt{3}\)
A. \(\frac{1}{2}\)
B. 1
C. \(\frac{\sqrt{3}}{2}\)
D. \(\sqrt{2}\)
E. \(\sqrt{3}\)
08 Apr 2021, 04:41
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twobagels
Suppose that quadrilateral PQRS has four congruent sides and satisfies PQ = PR. What is the value of \(\frac{QS}{PR}\)?
A. \(\frac{1}{2}\)
B. 1
C. \(\frac{\sqrt{3}}{2}\)
D. \(\sqrt{2}\)
E. \(\sqrt{3}\)
A. \(\frac{1}{2}\)
B. 1
C. \(\frac{\sqrt{3}}{2}\)
D. \(\sqrt{2}\)
E. \(\sqrt{3}\)
All sides are equal, making PQRS a rhombus. Now PR is a diagonal that is equal to the sides.
Thus PQR and PRS become equilateral triangle.
The diagonals PR and QS will bisect each other at 90.
\(\triangle PQO\) will make a 30-60-90 triangle with sides PO:OQ:PQ in ratio 1:\(\sqrt{3}\):2
So \(\frac{QO}{OP}=\frac{\sqrt{3}}{1}\)
\(\frac{2*QO}{2*OP}=\frac{\sqrt{3}}{1}\)
\(\frac{QS}{PR}=\sqrt{3}\)
E
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10 Jul 2022, 12:46
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twobagels
Suppose that quadrilateral PQRS has four congruent sides and satisfies PQ = PR. What is the value of \(\frac{QS}{PR}\)?
A. \(\frac{1}{2}\)
B. 1
C. \(\frac{\sqrt{3}}{2}\)
D. \(\sqrt{2}\)
E. \(\sqrt{3}\)
A. \(\frac{1}{2}\)
B. 1
C. \(\frac{\sqrt{3}}{2}\)
D. \(\sqrt{2}\)
E. \(\sqrt{3}\)
Let PQ=QR=RS=PS=PR=1 ( Given)
O is the midpoint of segment QS.
QO is height of equilateral triangle PQR.
Then QO = \(\frac{\sqrt{3}}{2}\).
So QS = \(\sqrt{3}\) ( QS = 2*QO)
\(\frac{QS}{PR}\) = \(\frac{\sqrt{3}}{1}\)
