Question : PQR is an equilateral triangle. MN is drawn parallel to QR such that M is on PQ and N is on PR. If PN = 6 cm, then the length of MN is:
Option 1: 3 cm
Option 2: 6 cm
Option 3: 12 cm
Option 4: 4.5 cm
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Correct Answer: 6 cm
Solution : Given: PQR is an equilateral triangle and MN is drawn parallel to QR MN || QR ∴ $\angle$PMN = $\angle$PQR and $\angle$PNM = $\angle$PRQ By AAA-similarity, $\triangle$PMN ~ $\triangle$PQR So, $\angle$PMN will also be an equilateral triangle. ⇒ MN = PN = PM = 6 cm. Thus, PN = 6 cm Hence, the correct answer is 6 cm.
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Question : A circle is inscribed in $\triangle $PQR touching the sides QR, PR and PQ at the points S, U and T, respectively. PQ = (QR + 5) cm, PQ = (PR + 2) cm. If the perimeter of $\triangle $PQR is 32 cm, then PR is equal to:
Question : In a ΔPRQ, AB is drawn parallel to QR, cutting sides at A and B where the length of PQ = 6 cm, length of QR = 8 cm, and length of QA = 3 cm. What is the length of AB?
Question : In a triangle PQR, S, and T are the points on PQ and PR, respectively, such that ST || QR and $\frac{\text{PS}}{\text{SQ}} = \frac{3}{5}$ and PR = 6 cm. Then PT is:
Question : The centroid of an equilateral triangle PQR is L. If PQ = 6 cm, the length of PL is :
Question : The centroid of an equilateral triangle PQR is L. If PQ = 6 cm, the length of PL is:
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