Question

Construct LMN such that LM = 6.6 cm, angle LMN = 60° and ND is the median and ND = 5 cm.

Answer 1

- Hint:Before solving this question, let us know how to make an angle of 60°.
The steps are given below:-
Below figure represents construction of Angle measuring 60 Degree with the help of Compass.

1) Use Ruler to draw a line segment QR of any convenient length.

2) Now, open your compasses to any convenient radius and with Q as the center draw an arc which cuts line segment QR at Y.

3). Again use your compasses and draw an arc with Y as center, which cuts the previous arc at X with the same radius as of step 2.

4) Now join QX and extend it to P.

Hence, we get an angle of 60°.


Complete step-by-step solution -

Let us now solve the question.
So, we need to construct a ∆LMN such that LM = 6.6 cm, angle LMN = 60° and ND is the median and ND = 5 cm.
We firstly need to draw a line segment LM of length 6.6 cm.

Now, we will construct an angle of 60° at M.
The steps for constructing an angle of 60° are provided in the hint above.

Now, we will draw the median ND measuring 5 cm.

Now, we will draw a line segment NL.

Hence, we have constructed the ∆LMN.

Note:-Let us now learn about the construction of an angle of 90°.
CONSTRUCTION OF A 90° ANGLE USING COMPASSES
Use Ruler and draw a Line segment BC of any convenient length.

Now use the compass and open it to any convenient radius. And with B as center, draw an arc which cuts line segment BC at Q.

     

Again use the compass and open to the same radius (as of step 2). And with Q as center, draw an arc which cuts the first arc at R.
        

Again use the compass and open to the same radius as of step 2. And with R as center, draw another arc which cuts the first arc at P.
    

Again use a compass of the same radius as of step 2 and with P and R as center draw two arcs which cut each other at E.

 Join OE and extend it to A.

           

Hence, the angle that we get is an angle of 90°