Mensuration

A. 27 m
B. 24 m
C. 18 m
D. 21 m
Let the length and the breadth of the floor be l m and b m respectively.
l = b + 200% of b = l + 2b = 3b
Area of the floor = 324/3 = 108 sq m
l b = 108 i.e., l * l/3 = 108
l2 = 324 => l = 18.

A. 8.5 m
B. 17 m
C. 34 m
D. 51 m
Let the breadth of the plot be b m.
Length of the plot = 3 b m
(3b)(b) = 867
3b2 = 867
b2 = 289 = 172 (b > 0)
b = 17 m.

A. 8
B. 12
C. 6
D. 2
Let the sides of the rectangle be l and b respectively.
From the given data,
(√l2 + b2) = (1 + 108 1/3 %)lb
=> l2 + b2 = (1 + 325/3 * 1/100)lb
= (1 + 13/12)lb
= 25/12 lb
=> (l2 + b2)/lb = 25/12
12(l2 + b2) = 25lb
Adding 24lb on both sides
12l2 + 12b2 + 24lb = 49lb
12(l2 + b2 + 2lb) = 49lb
but 2(l + b) = 28 => l + b = 14
12(l + b)2 = 49lb
=> 12(14)2 = 49lb
=> lb = 48
Since l + b = 14, l = 8 and b = 6
l – b = 8 – 6 = 2m.

A. 1 : 96
B. 1 : 48
C. 1 : 84
D. 1 : 68
Let the length and the breadth of the rectangle be 4x cm and 3x respectively.
(4x)(3x) = 6912
12×2 = 6912
x2 = 576 = 4 * 144 = 22 * 122 (x > 0)
=> x = 2 * 12 = 24
Ratio of the breadth and the areas = 3x : 12×2 = 1 : 4x = 1: 96.

A. 262 cm2
B. 384 cm2
C. 192 cm2
D. 131 cm2
Area of a parallelogram = base * height = 24 * 16 = 384 cm2

A. 225 cm2
B. 275 cm2
C. 285 cm2
D. 315 cm2
Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them) = 1/2 (20 + 18) * (15) = 285 cm2

A. 25 cm2
B. 42 cm2
C. 49 cm2
D. None of these
Area of a triangle = r * s
Where r is the inradius and s is the semi perimeter of the triangle.
Area of triangle = 2.5 * 28/2 = 35 cm2

A. 120 cm2
B. 130 cm2
C. 312 cm2
D. 315 cm2
The triangle with sides 26 cm, 24 cm and 10 cm is right angled, where the hypotenuse is 26 cm.
Area of the triangle = 1/2 * 24 * 10 = 120 cm2

A. 48√3 cm2
B. 128√3 cm2
C. 9.6√3 cm2
D. 64√3 cm2
Area of an equilateral triangle = √3/4 S2
If S = 16, Area of triangle = √3/4 * 16 * 16 = 64√3 cm2;