In a adjoining figure ABCD is a parallelogram with ab=6cm and ad=5cm. If DM is perpendicular to ab and the area of parallelogram ABCD is 24 cm square find the length of AM
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In the figure given below, ABCD is a parallelogram. AM⊥DC and AN⊥CB. If AM=6 cm,AN=10 cm and the area of parallelogram ABCD is 45 cm
2
, find
(i) AB
(ii) BC
(iii) area of △ADM : area of △ANB.
From the question it is given that,
ABCD is a parallelogram, AM⊥DC and AN⊥CB
AM=6cm
AN=10cm
The area of parallelogram ABCD is 45cm
2
Then, area of parallelogram ABCD=DC×AM=BC×AN
45=DC×6=BC×10
(i) DC=45/6
Divide both numerator and denominator by 3 we get,
=15/2
=7.5cm
Therefore, AB=DC=7.5cm
(ii) BC×10=45
BC=45/10
BC=4.5cm
(iii) Now, consider △ADM and △ABN
∠D=∠B … [because opposite angles of a parallelogram]
∠M=∠N … [both angles are equal to 90∘ ]
Therefore, △ADM∼△ABN
Therefore, area of △ADM/area of △ABN=AD
2 /AB
2=BC
2 /AB 2
=4.52/7.52
=20.25/56.25
=2025/5625
=81/225
=9/25
Therefore, area of △ADM : area of △ANB is 9:25