Areas

The Length of a plot is four times is breadth. A playground measuring 1200 square meters occupies a third of the total area of the plot. What is the length of the plot in meters?

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The Length of a plot is four times is breadth. A playground measuring 1200 square meters occupies a third of the total area of the plot. What is the length of the plot in meters?

A. 20
B. 30
C. 60
D. None of these

Explanation:
Area of the plot = (3×1200)Sq.m = 3600 Sq.m
Breadth = x meters and length = 4x meters
4x × x = 3600 or x2 = 900 0r x = 30
Length of plot = 4x = (4×30) m = 120 m

A big rectangular plot of area 4320 Sq.m is divided into 3 square shaped smaller plots by fencing parallel to the smaller side of the plot. However, some area of land was still left as a square plot could not be formed. So 3 more square shaped plots were formed by fencing parallel to the longer side of the original plot. Such that no area of the plot was left a surplus. What are the dimensions of the original plot?

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A big rectangular plot of area 4320 Sq.m is divided into 3 square shaped smaller plots by fencing parallel to the smaller side of the plot. However, some area of land was still left as a square plot could not be formed. So 3 more square shaped plots were formed by fencing parallel to the longer side of the original plot. Such that no area of the plot was left a surplus. What are the dimensions of the original plot?

A. 160m × 27m
B. 240m × 18m
C. 120m × 36m
D. 135m × 32m
Let the side of smaller square at the extreme right be a

Then side of the larger square is 3a

Total area of the field = a2 + a2 +a2 + (3a)2 +(3a)2 = 30a2

Therefore, 30 a2 = 4320 => a2 = 432 / 3 = 144 => a = 12

Smaller side of the field = 36

Larger side of the field = (3a) × 3 + a = 10 a = 10 × 12 = 120

Original Dimensions of the field = 120m × 36m

Which one of the following has a greater perimeter than the rest?

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Which one of the following has a greater perimeter than the rest?

A. A square with an area of 36 sq.cm
B. An Equilateral Triangle with a side of 9 cm
C. A rectangle with 10 cm as length and 40 sq.cm as area
D. A circle with a radius of 4 cm

Explanation:
From Option (A), Area of Square = 36 Sq.cm
Therefore, Side of Square = √36 = 6 cm And
Perimeter of square = 4 × 6 = 24 cm
From option (B), Side of an Equilateral Triangle = 9 cm
Therefore, Perimeter of triangle = 3 × 9 = 27 cm
From Option (C), Length of rectangle , l= 10 cm And
Area of Rectangle = 40 Sq.cm
Let Breadth of Rectangle, b = 40/10 = 4 cm
Therefore, Perimeter of rectangle = 2(10 + 4) = 28 cm
From Option (D), Radius of Circle = 4 cm
Therefore Circumference of circle = 2 × 3.14 × 4 = 25.12 cm
So, Rectangle with 10 cm as length and 40 Sq.cm as an area has a greater perimeter than the rest.

A paper is in a square form whose one side is 20 cm. Two semi circles are drawn on its opposites as diameters. If these semi circles are cut down what is the area of the remaining paper?

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A paper is in a square form whose one side is 20 cm. Two semi circles are drawn on its opposites as diameters. If these semi circles are cut down what is the area of the remaining paper?

A. (400 – 100π) cm2</sup
B. (400 – 2π) cm2</sup
C. (400 – 200π) cm2</sup
D. 200π cm2</sup