Area and Perimeter- 2 - Free MCQ Practice Test with solutions, SSC CGL

Other side = √5 ² - 4²
= √ 9
=3 m

So The area of the rectangular field = 4 x 3
= 12 m²

Let breadth = b meters.
Then, length = 4b/3 meters.
∵ b x 4b/3 = 300

⇒ b2 = 300 x 3/4
⇒ b2 = 225
∴ b = 15

Hence, required difference = [(Length) - (Breadth) ]
= 4b/3 - b
= b/3
= 15/3 m
= 5 m

Let breadth = b meters.
then, length = 3b/2 meters
∴ b x 3b/2 = 2/3 X 10000
⇒ b2 = (4 x 10000)/9
⇒ b = ( 2 X 100)/3 m
∴ Length = (3/2) x (2/3) x 100 m
= 100 m

Area of the square = (84 + 84) m²
Area of the rectangle = (144 x width) m²

From question both area would be same,
∴ Width = (84 x 84) / 144 m = 49 m

Let the length, breadth and height of the room be l, b and h respectively

As per question
Cost of 2(l + b) x h = Rs. 48
∴ Required cost = cost of 2 (2l + 2b) x 2h
= cost of 4 [2(l + b) x h ]
= 4 x Rs. 48
= Rs. 192

Area of four walls = 2 x (l + b ) x h
⇒ 2 x (7.5 + 3.5 ) x h = 77 m²
⇒ h = 77 / (2 x 11) = 7/2
∴ h = 3.5 meters

Let the width of the room be x members
Then, its area = (4x) m²
Area of each new square room = (2x)m²
Let the side of each new room = y meters
Then, y² = 2x
Clearly, 2x is a complete square when x=2
∴ y² = 4
⇒ y = 2 m . 

Area of verandah = [(25 x 20) -(20 x 15)] m²
= 200 m²
∴ Cost of flooring = Rs. (200 x 3.50)
= Rs. 700 

Let the area of square be (9x)² m² and (x²) m²
Then, their sides are (3x) m and x metres respectively
∴ Ratio of their perimeters = 12x / 4x
=3:1 

Let the side of the square = y cm
Then, breadth of the rectangle = 3y/2 cm
∴ Area of rectangle = (40 x 3y/2) cm²
= 60y cm²
∴ 60y = 3y²
∴ y = 20
Hence, the side of the square = 20 cm

Original area = (22/7) x 9 x 9 cm²
New area = (22/7) x 7 x 7 cm²
∴ Decrease = 22/7 x [(9)² -(7)²] cm²
=(22/7) x 16 x 2 cm²
Decrease percent = [(22/7 x 16 x 2) /( 7/22 x 9 x 9)] x 100 %
= 39.5 % 

∵ 22/7 x r² = 13.86 x 10000
⇒ r² = (13.86 x 10000 x 7) / 22
∴ r = 210 m
⇒ Circumference = [2 x (22/7) x 210 ] m
= 1320 m
Cost of fencing = Rs. (1320 x 20)/100
= Rs . 264 

circumference = 2πr = 2 x (22 / 7) x r = 352
⇒ r = (352 x 7) / (22 x 2) =56 cm
Now area = πr² = (22 / 7) x 56 x 56 m²
= 9856 m² 

circumference = 2πr = 2 x (22 / 7) x r = 352
⇒ r = (352 x 7) / (22 x 2) =56 cm
Now area = πr² = (22 / 7) x 56 x 56 m²
= 9856 m² 

∵ s= (13 + 5 + 12) / 2 cm
= 15cm
s-a = 2 cm,
s-b = 10 cm and
s-c = 3 cm
⇒ Area = √ (15 x 2 x 10 x 3 ) cm²
= 30 cm²
⇒ (12 x h) / 2 = 30
∴ h = 5 cm