Q. 15.0( 4 Votes )

Construct each of

Answer :

Step 1:


Draw a line XY=10.4 i.e. the perimeter.



Step 2:


Construct an angle equal to B=45° and another angle equal to C=120°



Step 3:


Bisect these angles and name the intersecting point as A.



Step 4:


Construct perpendicular bisectors of AX and AY and name the PQ and RS respectively.



Step 5:


Name the intersecting point of PQ and XY as B and RS the intersecting point of RS and XY as C.


Join AB and AC.



ABC is the required triangle.


Justification


As B is on line PQ which is the perpendicular bisector of AX,


AB+BC+CA = XB+BC+CY=XY


Then,BAX=AXB (as in triangle AXB, AB is equal to XB)


As ABC is the external angle of triangle AXB


Then,ABC=BAX + AXB(exterior angle sum property)


ABC=AXB+AXB


ABC=2AXB=45° or B.


Similarly,


ACB=2CAY=120° or C.


Thus the construction is justified.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses