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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