Question

In perpendicular quadrilateral ABCD, the perpendicular to the base AB is DX and the perpendicular to the base BC is AY. If AB = 20 cm, = DX = 12 cm and AY = 15 cm, find BC and find the perimeter of ABCD​

Answer 1

Answer:

Given AB=20cm,AD=12cm

DC=AB=20cm and AD=BC=12cm

Given that bisector of ∠A intersects DC at E and BC produced at F.

Draw PF∥CD

From the figure, CD∥FP and CF∥DP

Hence PDCF is a parallelogram.

AB∥FP and AP∥BF

ABFP is also a parallelogram

Consider △APF and △ABF

∠APF=∠ABF [Since opposite angles of a parallelogram are equal]

AF=AF (Common side)

∠PAF=∠AFB (Alternate angles)

△PAF≅△BFA (By ASA congruence criterion)

AB=AP

AB=AD+DP

=AD+CF [Since DCFP is a parallelogram]

CF=AB−AD

=(20−12)cm=8cm