In the figure, D1, D2, D3 .... are points on ray DM at equal distances and D3P || D-E. What
will be the ratio of DE to DP?
Answers
Given : D₁ , D₂ , D₃ ..... are points on ray DM at equal distances and D₃P || D₇E
To Find : ratio of DE to DP
Solution:
if a line is drawn parallel to one side of a triangle intersecting the other two sides, then it divides the two sides in the same ratio.
in ΔDD₇E
D₃P || D₇E
=> DD₃/D₃D₇ = DP/PE
D₁ , D₂ , D₃ , D₄, D₅ , D₆ , D₇ are at at equal distance
Hence DD₃ = 3X
DD₇ = 7X
=> D₃D₇ = 4X
=> 3X / 4X = DP/PE
=> 3/4 = DP/PE
=> PE/DP = 4/3
Adding both sides
=> PE/DP + 1 = 4/3 + 1
=> (PE + DP)/DP = 7/3
=> DE/DP = 7/3
ratio of DE to DP = 7/3
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7/3 = 7:3
DE = 7 units
DP = 3 units