1.

Construct a Delta ABC in which BC=5.6 cm, angleB=30^(@) and (AB-AC)=3 cm. Measure AB and AC. Justify your construction.

Answer»

Solution :STEPS OF CONSTRUCTION
(i) Draw `BC=5.6` cm.
(ii) Construct `angleCBX=30^(@)`.
(III) ALONG `BX`, set off `BD=3` cm.
(iv) Join `CD`.
(v) Draw the right bisector of `CD`, meeting `BD` produced at `A`.
(vi) Join `AC`.
Then, `Delta ABC` is the required triangle.
Verification :
On measuring, we FIND that `AB=6.1` cm and `AC=3.1` cm.
`:. (AB-AC)=(6.1-3.1) cm =3` cm.
Justification :
Since `A` lies on the perpendicular bisector of `CD`, we have `AD=AC`.
Now, `BD=3` cm `implies AB-AD=3` cm
`implies AB-AC=3 cm ""[ :' AD=AC]`
HENCE, `Delta ABC` is the required triangle.


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