Question) Construct an isosceles triangle with perimeter as 12 cm and height as 3 cm - Maths - Constructions

Question

Question) Construct an isosceles triangle with perimeter as 12 cm
and height as 3 cm

Rishabh Mittal · Accepted Answer

Dear Student ,

Please find below the solution to the asked query :

Steps of construction :1 Draw a line segment XY=12 cm
2 Draw perpendicular bisector of XY and cut off it at 3 cm and name it as AD
3 Join AX and AY 
4 Draw perpendicular bisector of AX and AY 
5 The point of intersection of bisectors of AX and AY at CY be  B and C
6 Join AB and AC
Thus , △ABC is the required triangle

Justification:In △BPX and △BPAPX=PA        Since BP is perpendicular bisector∠BPX=∠BPA     Each 90°BP=BP    CommonBy SAS congruency criterion△BPX ≅ △BPABX=BA   
 1Similarly , In △CQY and △CQACY=CA   
 2Now ,XY=12 cm   By constructionBX+BC+CY=12BA+BC+CA=12       Using 1 and 2Perimeter of △ABC=12 cm 
Hence Proved 
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Question) Construct an isosceles triangle with perimeter as 12 cm and height as 3 cm.