Mathematics
Construct a triangle BCP with BC = 5 cm, BP = 4 cm and ∠PBC = 45°. Complete the rectangle ABCD, such that :
(i) P is equidistant from AB and BC.
(ii) P is equidistant from C and D.
Measure and record the length of AB.
Constructions
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Answer
Steps of construction :
Draw a line segment BC = 5 cm.
With B as center draw an arc BX, at an angle of 45°.
From BX cut off BP = 4 cm.
Join PC. Hence, BPC is the required triangle.
Draw perpendiculars at points B and C.
With P as center and radius PC, cut an arc on the perpendicular on C at D.
From D, draw a line parallel to BC which intersects the perpendicular on B at A.
Hence, ABCD is the required rectangle.
On measuring we get,
AB = 5.7 cm
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