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In the given figure, PQRS is a parallelogram. If X and Y are mid-points of PQ and SR respectively and diagonal Q is joined. The ratio ar (||gm XQRY) : ar (ΔQSR) = - Mathematics

MCQ

In the given figure, PQRS is a parallelogram. If X and Y are mid-points of PQ and SRrespectively and diagonal Q is joined. The ratio ar (||gm XQRY) : ar (ΔQSR) =

Options

  •  1 : 4

  •  2 : 1

  •  1 : 2

  • 1 : 1

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Solution

Given: (1) PQRS is a parallelogram.

(2) X is the midpoint of PQ.

(3) Y is the midpoint of SR.

(4) SQ is the diagonal.

To find: Ratio of area of ||gm XQRY : area of ΔQRS.

Calculation: We know that the triangle and parallelogram on the same base and between the same parallels are equal in area.

∴ Ar (||gm PQRS) = Ar (ΔQRS)

`Ar ( "||"^(gm) XQRY ) = 1/2 Ar ("||"^(gm) PQRS)`

(since X is the mid point of PQ and Y is the midpoint of SR)

`Ar ("||"^(gm) XQRY) = Ar (ΔQRS)`

`Ar ("||"^(gm) XQRY ) : Ar (ΔQRS) = 1:1`

 

 

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APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 14 Areas of Parallelograms and Triangles
Q 14 | Page 61
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