InterviewSolution
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InterviewSolution
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Construct a triangle with sides 5 cm, 6 cm and 7 cm and then another triangle whose sides are 7/5 of the corresponding sides of the first triangle. |
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Answer» Solution :Steps of Construction : 1. Draw a line segment BC = 5 cm. 2. Taking B and C as centres draw two ARCS of radii 7 cm and 6 cm interecting each other at A. 3. JOIN BA and CA, `DeltaABC` is the required triangle. 4. From B draw any RAY BX downwared making an acute `angleCBX.` 5. Locate seven points `B_(1),B_(2),B_(3),B_(4),B_(5),B_(6)and B_(7)` on BX, such that `BB_(1)=B_(1)B_(2)=B_(2)B_(3)=B_(3)B_(4)=B_(4)B_(5)=B_(5)B_(6)=B_(6)B_(7).` 6. Join `B_(5)C` and from `B_(7)` draw a line `B_(7)M"||"B_(5)C` interecting the EXTENDED line segment BC at M. 7. From point M draw `MN"||"CA` intersecting the extended line segment BA at N. Then, `DeltaNBM` is the required triangle whose sides are `7/5` of the corresponding sides of `DeltaABC.`  Justifiction : By construction, `B_(7)M"||"B_(5)C` `therefore""(BC)/(CM)=5/2` `Now,""(BM)/(BC)=(BC+CM)/(BC)=1+2/5=7/5` `therefore""(BM)/(BC)=7/5` `Also,""MN"||"CA` `therefore""DeltaABC~DeltaNBM` `and""(NB)/(AB)=(BM)/(BC)=(MN)/(CA)=7/5` |
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