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InterviewSolution
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Draw a DeltaABC in which AB=5 cm, BC= 6 cm and angleABC=60^(@). Construct a triangle similar to ABC with scale factor (5)/(7). Justify the construction. |
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Answer» Solution :Steps of construction 1. Draw a LINE segment AB=5 cm . 2. From point B, draw `angleABY=60^(@)` on which take BC= 6 cm. 3. Join AC , `DeltaABC` is the required triangle. 4. From A, draw any ray AX downwards making an acute angle. 5. Mark 7 point `B_(1),B_(2),B_(3),B_(4),B_(5),B_(6) " and " B_(7)` on AX, Such that `AB_(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_(7)B` and from `B_(5)` draw `B_(5)M||B_(7)B` intersecting AB at M. From point M draw MN||BC intersecting AC at N. Then, `DeltaAMN` is the required triangle WHOSE sides are EQUAL to `(5)/(7)` of the CORRESPONDING sides of the `DeltaABC`. Justification Here , `B_(5)M||B_(7)B` ( by construction ) `:. (AM)/(MB)=(5)/(2)` Now, `(AB)/(AM)=(AM+MB)/(AM)` `=1+(MB)/(AM)=1+(2)/(5)=(7)/(5)` Also, MN||BC `:. DeltaAMN ~DeltaABC` Therefore, `(AM)/(AB)=(AN)/(AC)=(NM)/(BC)=(5)/(7)` 
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