14. ABCD is a rhombus with side equal to 8 cm. CB is produced to R
such that BR-4 cm. DR cuts AC and AB at P and respectively.
ar(ADP)
ar(APCR)
ar{ ADP)
(c)
ar(ADCP)apq
(DCP)k
ar(APO)
ar(ADP)
(d)
ar( ZAPO)
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Answer:
DR can cut AB at only one point say P.
Since P lies on AB it follows that PB is || DC. Hence triangle RBP ~triangle RCD. And since BR:CR = 4:8 = 1:2 it follows that PB:DC is also 1:2 Therefore PB = 4 cms. So P is the midpoint of AB. Area of triangle ADP is half the area of triangle ADB. And since area of triangle ADB = area of triangle BCD = area of triangle DCP it follows that area of triangle ADP = one-half the area of triangle DCP.
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