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Question

Construct a triangle with 3 cm base and sum of other two sides is 8 cm and one base angle is 60o.

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Solution

Given the base BC of the triangle ABC be 3 cm, one base angle B=60o and the sum of the other two sides be 8 cm i.e, AB + AC = 8 cm.
STEPS :
(i) Draw BC = 3 cm
(ii) At point B, draw PB so that PBC=60o
(iii) From BP, cut BC = 8 cm.
(iv) Join D and C.
(v) Draw perpendicular bisector of CD, which meets BD at point A.
(vi) Join A and C.

Thus, ABC is the required triangle.
Proof : Since, OA is perpendicular bisector of CD
OC = OD
AOC = AOD = 90°
Also, OA = OA [Common]
AOC AOD [By SAS]
AC = AD
BD = BA + AD
= BA + AC
= Given sum of the other two sides
Thus, base BC and B are draw as given and BD = AC.
Hence Proved

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