Using ruler and compasses only, construct a Δ ABC from the following data: AB+BC+CA =12 cm, ∠ B = 45° and ∠ C = 60°.

Question

Using ruler and compasses only, construct a &#x394; ABC from the following data: AB+BC+CA =12 cm, &#x2220; B = 45&#xB0; and &#x2220; C = 60&#xB0;.

Philoid · Accepted Answer

We are asked to construct a triangle XYZ such that

We will follow the following algorithm for the construction

Steps of construction-

STEP1: Draw a line segment XY of length 11 cm.

STEP2: Draw DXY = 45° and ∠EYX =60°

STEP3: Bisect DXY and EYX and mark the point of intersection of these angle bisectors by A.

STEP4: Draw perpendicular bisectors of AX and AY. They meet XY at point B and C, respectively.

STEP5: Draw AB and AC to get the desired triangle ABC.