ABCD is a parallelogram AD, AE are the altitudes from A to the opposite sides. If AD = 7 cm, AE = 12 cm and the area of ABCD = 105 cm, find the perimeter of ABCD.
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In △AFE and △BFC,
∠AFE=∠BFC (Common angle)
∠AEF=∠BCF (Corresponding angles of parallel lines)
∠FAE=∠CBF (Corresponding angles of parallel lines)
Thus, △AFE∼△CFB (AAA rule)
Hence,
BF
AF
=
BC
AE
AF+AB
AF
=
BC
AE
8+12
8
=
BC
4
BC=
8
4×20
BC=10 cm
Perimeter of parallelogram = AB+BC+BC+AD
Perimeter of parallelogram = 2(AB+BC)
Perimeter of parallelogram = 2(12+10) (Opposite sides are equal)
Perimeter of parallelogram = 44 cm
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0
Answer:
120 cm
Thank you to see
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