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Parallelogram A B C D and rectangle A B ...

Parallelogram `A B C D` and rectangle `A B E F` have the same base `A B` and also have equal areas. Show that the perimeter of the parallelogram is greater than that of the rectangle.

Text Solution

Verified by Experts

AB=DC-(1)
AB=EF-(2)
DC=EF
adding equation 1 and 2
AB+DC=AB+EF-(3)
`BEltBC`and`AFltAD`
`BC>BE` and`ADltAF`
BC+AD>BE+AF-(4)
...
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RD SHARMA ENGLISH-AREA OF PARALLELOGRAMS AND TRIANGLES-All Questions
  1. A B C D is a parallelogram X and Y are the mid-points of B C and C D r...

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  2. The area of a trapezium is half the product of its height and the su...

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  3. Parallelogram A B C D and rectangle A B E F have the same base A B and...

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  4. O is any point on the diagonal B D of the parallelogram A B C D. Prove...

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  5. Prove that the area of a rhombus is equal to half the rectangle cont...

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  6. A quadrilateral A B C D is such that diagonal B D divides its area in ...

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  7. Prove that two triangles having the same base and equal areas lie betw...

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  8. Show that a median of a triangle divides it into two triangles of eq...

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  9. A B C D is a trapezium with A B || D C. A line parallel to A C inters...

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  10. Diagonals A C and B D of a quadrilateral A B C D intersect at O in suc...

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  11. Let A B C D be a parallelogram of area 124c m^2dot If E and F are the ...

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  12. If A B C D is a parallelogram, the prove that a r( A B D)=a r( B C D...

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  13. Triangles on the same base and between the same parallels are equal ...

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  14. Triangles having equal areas and having one side of one of the trian...

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  15. In Figure, A B C D is a parallelogram and E F C D is a rectangle. Al...

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  16. If E ,F ,G and H are respectively the mid-points of the sides of a ...

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  17. In Figure, P is a point in the interior of a parallelogram A B C D . S...

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  18. In Figure, P Q R S and A B R S are parallelograms and X is any point o...

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  19. The diagonals of a parallelogram A B C D intersect at a point Odot Thr...

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  20. E , F , G , H are respectively, the mid-points of the sides of parall...

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