Problems on Areas : Aptitude Test

  • 1. The sides of a rectangle are in the ratio of 6 : 5 and its area is 1331 sq.m. Find the perimeter of rectangle.
A.) 120 m
B.) 121 cm
C.) 121 m
D.) None of these

Answer: Option 'C'

Let 6x and 5x be sides of the rectangle 
6x × 5x = 1331 
11x2 = 1331 
x2 = 1331/11 = 121 => x = 11 
Length = 6x = 6 × 11 = 66 
Breadth = 5x => 5 × 11 = 55 
Perimeter = 2 (l+b) => 2 (66+55) = 121 m

  • 2. A rectangle measures 8 Cm on length and its diagonal measures 17 Cm. What is the perimeter of the rectangle? 
A.) 46 cm
B.) 48 cm
C.) 46 m
D.) None of these

Answer: Option 'C'

Second side = √172-82 
= √289-64 
= 15 cm 
Perimeter = 2 (l+b) = 2(8+5) Cm = 2(23) = 46 Cm

  • 3. A rectangular courtyard 3.78 m lang and 5.25 m broad is to be paved exactly with square tiles, all of the same size. The minimum number of such tiles is: 
A.) 350
B.) 450
C.) 460
D.) 470

Answer: Option 'B'

l = 378 Cm and b = 525 Cm 
Maximum length of a square tile 
= HCF of (378,525) = 21 Cm 
Number of tiles = (378×525)/(21×21) = (18×25) = 450

  • 4. The ratio of the areas of two squares, one having double its diagonal then the other is:
A.) 1 : 3
B.) 3 : 1
C.) 1 : 4
D.) 4 : 1

Answer: Option 'D'

Lenth of the diagonals be 2x and x units. 
areas are 1/2 × (2x)2 and (1/2 × x2
Required ratio = 1/2 × 4 x2 : 1/2 x2 = 4 : 1

  • 5. A rectangular mat has an area of 120 sq.metres and perimeter of 46 m. The length of its diagonal is: 
A.) 17 cm
B.) 17 m
C.) 17 m2
D.) 16 m

Answer: Option 'B'

rectangular area = l × b = 120 and perimeter = 2(l+b) = 46 
l+b = 23 
(l-b)2 - 4lb = (23)2 - 4 × 120 = (529-480) = 49 = l-b = 7
l+b = 23, l-b = 7, we get l = 15, b = 8 
Diagonal = √152+82 
√225+64 => √289 = 17 m