Mensuration

Question

A square and a rectangular field with measurements as given in the figure have the same perimeter. Which field has a larger area?

Solution

(a) Side of the square = 60 m
∴ Its perimeter = 4 x side
= 4 x 60 m
= 240 m
Area of the square = Side x Side
= 60 m x 60 m
= 3600 m²
(b) ∵ Perimeter of the rectangle = Perimeter of the given square
∴ Perimeter of the rectangle = 240 m
or 2 x [Length + Breadth] = 240 m
or 2 x [80 m + Breadth] = 240 m
or 80 m + Breadth = $240 over 2 straight m space equals space 120 space straight m$
∴ Breadth = (120 - 80) m = 40 m
Now, Area of the rectangle = Length x Breadth
= 80 m x 40 m
= 3200 m²
Since, 3600 m² > 3200 m²
∴ Area of the square field (a) is greater.

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Mensuration

A square and a rectangular field with measurements as given in the figure have the same perimeter. Which field has a larger area?

Some More Questions From Mensuration Chapter

A parallelogram is divided into two congruent triangles by drawing a diagonal across it. Can we divide a trapezium into two congruent triangles?

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