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The dimensions of a rectangle are 51 m and 49 m respectively while side of a square is 50 m. Which of the following statements is correct ?
Options:
A .  Diagonal of the square and the rectangle are equal.
B .  Diagonal of both the geometrical figures intersect at right angles.
C .  The perimeters of both the geometrical figure are equal.
D .  Both the geometrical figures are of the same area.
Answer: Option C
(A) Diagonal of the rectangle :
$$\eqalign{
& = \sqrt {{{\left( {51} \right)}^2} + {{\left( {49} \right)}^2}} m \cr
& = \sqrt {2601 + 2401} \,m \cr
& = \sqrt {5002} \,m \cr} $$
Diagonal of the square :
$$\eqalign{
& = 50\sqrt 2 \,m \cr
& = \sqrt {5000} \,m \cr} $$
(B) Diagonal of a square intersect at right angles but those of a rectangle do not.
(C) Perimeter of rectangle :
= 2(51 + 49) m
= 200 m
Perimeter of square :
= (4 × 50) m
= 200 m
(D) Area of rectangle :
= (50 × 50) m2
= 2500 m2

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