Construct each of

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.

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