# Construct ΔABC, in which BC= 5.2cm, ∠C = 45° and perimeter of ΔABC is 10 cm.

Given: base BC= 5.2cm, C = 45° of ΔABC and

perimeter of ΔABC = 10 cm.

Required: To construct a ΔABC

Steps of construction:

i: Draw a segment BC of length of 5.2cm.

ii: At vertex C, construct C = 45° and produce a ray P’C

iii: Mark an arc on ray CP cutting at D such that CD = 4.8cm.

iv: Draw segment DB.

v: Construct the perpendicular bisector of segment DB.

vi: Name the point of intersection of ray CP and the perpendicular bisector of DB as A.

vii: Draw segment AB.

ΔABC is the required triangle.

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