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Question

# A triangle and a parallelogram are on the same base and between the same parallel lines they have:

A
Equal area
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B
Equal perimeter
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C
Both
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D
None of these
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Solution

## The correct option is B None of these⇒ Let △ABP and a parallelogram ABCD be on the base AB and between the same parallels AB abd PC.⇒ Draw BQ∥AP to obtain another parallelogram ABQP and ABCD are on the same base AB and between the same parallel AB and PC.∴ ar(ABQP)=ar(ABCD) ---------- ( 1 )⇒ But △PAB ≅ △BQP [Diagonals PB divides parallelogram ABQP into two congruent triangles.]⇒ So ar(PAB)=ar(BQP) ----------- ( 2 )∴ $ar(PAB)=ar(ABQP) ----------- ( 3 ) [From ( 2 )]This gives ar(PAB)=12ar(ABCD) [From ( 1 ) and ( 3 )]⇒ So, we have prove that a triangle and a parallelogram are on same base and between the same parallel lines they don't have equal area or equal perimeter.⇒ So, correct answer is option D. Suggest Corrections 0 Join BYJU'S Learning Program Related Videos Triangles on the Same Base (Or Equal Bases) and Equal Areas Will Lie between the Same Parallels_$008
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