Question

In the figure, PQRV is a trapezium in which seg PQ || seg VR, SR=4 and PQ = 6.Find VR.​

Answer 1

Answer:

It answer is 17cm. (approx.)

Answer 2

In the figure, PQRV is a trapezium in which seg PQ || seg VR, SR=4 and PQ = 6.

$1) In \:right \triangle QSR ,\\\angle {RQS}= 45\degree ,\: SR = 4$

$tan \:45\degree = \frac{SR}{QS}$

$\implies 1 = \frac{4}{QS}$

$\implies QS = 4$

$PT = QS = 4$

$2) In \: right \triangle PTV , \\\angle VPT = 60\degree$

$tan \: 60\degree = \frac{VT}{PT}$

$\implies \sqrt{3}= \frac{VT}{4}$

$\implies 4\sqrt{3} = VT$

$3) \red { Value \:of \: VR} = VT + TS + SR \\=VT + PQ + SR \\= 4\sqrt{3} + 6 + 4\\ = 4\times 1.732 + 10 \\= 6.928 + 10 \\= 16.928$

Therefore.,

$\red {Value \:of \: VR} \green { = 16.928}$

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