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141. Area of a circle inscribed in an equilateral triangle is 616 sq cm. Find the side of the equilateral triangle.
  A.  25√3 cm
  B.  28√3 cm
  C.  29√3 cm
  D.  27√2 cm
     
   
View Answer

Shortcut:
If the area of a circle inscribed in an equilateral triangle is 'z' sq units, then the side of the equilateral triangle is
√(
12z / π
)
units.
Here, z = 616
Using this value in the shortcut, we get:
Required side =
√(
12 x 616 / 22/7
)

=
√(
12 x 616 x 7 / 22
)

= √(12 x 28 x 7) = 28√3
Hence, the side of the equilateral triangle is 28√3 sq cm.

142. Find the numbers of diagonals of a hexagon.
  A.  9 diagonals
  B.  7 diagonals
  C.  4 diagonals
  D.  5 diagonals
     
   
View Answer

Shortcut:
There is a relation between the number of sides and the number of diagonals in a polygon. The relationship is given below.
Number of diagonals =
n(n − 3) / 2
.
where, n = No. of sides of polygon
Here, n = 6
Using this value in the shortcut, we get:
Required numbers of diagonals =
6(6 − 3) / 2

=
6 x 3 / 2
= 3 x 3 = 9
Hence, there will be 9 diagonals of the hexagon.

143. The area of a rectangular plot is 14 times its breadth. If the difference between the length and the breadth is 9 metres, what is its breadth?
  A.  2 m
  B.  4 m
  C.  6 m
  D.  5 m
     
   
View Answer

Shortcut:
The area of a rectangular plot is 'a' times its breadth. If the difference between the length and breadth is 'b' metres, then the breadth is given by (a − b) metres.
Note: If instead of difference, sum of the length and breadth is given, breadth is given by (b − a) metres. Here 'a' will be always less than 'b'.
Here, a = 14, b = 9
Using this value in the shortcut, we get:
Breadth = (14 − 9) = 5
Hence, the breadth is 5 metres.

144. The length and the breadth of the floor of a room is 20 ft and 10 ft respectively. Square tiles of 2 ft dimentsion having three different colours are placed on the floor. The first row of tiles on all sides is of black colour, out o the remaining one-third is of white colour and the remaining are of blue colour. How many blue-colour tiles are there?
  A.  12 tiles
  B.  14 tiles
  C.  16 tiles
  D.  18 tiles
     
   
View Answer

Area covered by black tiles = (20 + 20) x 2 + (6 + 6) x 2 = 80 + 24 = 104 sq ft

Area of the floor PQRS = 20 x 10 = 200 sq ft
∴ Remaining area = 100 − 104 = 96 sq ft
∴ Area covered by white tiles =
1 / 3
x 96 = 32 sq ft.
∴ Area covered by blue tiles = 96 − 32 = 64 sq ft
∴ Number of blue-color tiles =
64 / 2 x 2
= 16

145. The squared value of the diagonal of a rectangle is (64 + B2) sq cm, where B is less than 8 cm. What is the breadth of that rectangle?
  A.  2 cm2
  B.  6 cm2
  C.  4 cm2
  D.  8 cm2
     
   
View Answer

(Diagonal)2 = 64 + B2
or, 102 = 64 + 62
∴ B = 6
Hence, the breadth of that rectangle is 6 sq cm.

146. A rectangular plate is of 6 m breadth and 12 m length. Two apertures of 2 m diameter each and one aperture of 1 m diameter have been made with the help of a gas cutter. What is the area of the remaining portion of the plate?
  A.  60.93 sq m
  B.  62.93 sq m
  C.  64.93 sq m
  D.  66.93 sq m
     
   
View Answer

Required area =
[
6 x 12 −  
{
2 x π
(
2 / 2
)
2 + π
(
1 / 2
)
2
}]

=
[
72 −  
{
2 x π + π
(
1 / 4
)}]

= 72 −  
{
2π +
π / 4
}

= 72 −
9π / 4

= 72 −
9 / 4
x
22 / 7

= 72 −
99 / 14
= 72 − 7.07 = 64.93
Hence, the area of the remaining portion of the plate is 64.93 sq m.

147. The length and the breadth of a rectangle are in the ratio of 3 : 2 respectivvely. If the sides of the rectangle are extended on each side by 1 metre, the ratio of length to breadth becomes 10 : 7. Find the area of the original rectangle in square metres.
  A.  210 sq m
  B.  212 sq m
  C.  214 sq m
  D.  216 sq m
     
   
View Answer

Let the length and the breadth be 'L' and 'B' respectively
L / B
=
3 / 2

or, L =
3 / 2
B ------------ eq (i)
L + 2 / B + 2
=
10 / 7

or, 7L − 10B = 6 ------------ eq (ii)
From eq(i), we get:
10.5B − 10B = 6
or, 0.5B = 6
or, B =
6 / 0.5
= 12
L =
3 / 2
x 12 = 18
Area = L x B = 18 x 12 = 216 sq m

148. The area of a right-angled triangle is two-third of the area of a rectangle. The base of the triangle is 80 percent of the breadth of the rectangle. If the perimeter of the rectangle is 200 cm, what is the height of the triangle?
  A.  800 cm
  B.  Date inadequate
  C.  600 cm
  D.   400 cm
     
   
View Answer

Let the base and height of triangle, and length and breadth of rectangle be L and h and L1 and b1 respectively.
Then,
1 / 2
x L x h =
2 / 3
x L1 x b1 ------------- eq(i)
or, L =
4 / 5
b1 ------------ eq (ii)
and L1 + b1 = 100 -----------------eq (iii)
In the above we have three equations and four unknowns.
Hence the value of 'h' can't be determined.

149. Four sheets of 50 cm x 5 cm are to be arranged in such a manner that sa square could be formed. What will be the area of inner part of the square so formed?
  A.  2025 sq cm
  B.  2020 sq cm
  C.  2035 sq cm
  D.  2045 sq cm
     
   
View Answer

The four sheets are BMRN, AMQL, NSKC and DLPK

∴ Side of the new square sheet = 50 + 5 = 55 cm and side of the inner part of the square (55 − 10) = 45 cm
Hence, area = (45)2 = 2025 sq cm.

150. The expenses of carpeting a hall room were Rs 54000, but if the length had been 2 m less than it was, the expenses would have been Rs 48000. What was the length?
  A.  13 m
  B.  15 m
  C.  18 m
  D.  20 m
     
   
View Answer

Let the length be 'a' m and breadth be 'b' metre.
Then Area = a x b sq m
Cost of carpeting per sq m = Rs
54000 / a x b
------------- eq(i)
In the second case length is reduced by 2 metre
i.e., Area = (a − 2) b sq metre.
Cost of carpeting per sq m =
48000 / (a − 2)b
------------ eq (ii)
Now, from the question, we have
54000 / ab
=
48000 / (a − 2)b

54000(a − 2)b = 48000(ab)
9(a − 2) = 8a
9a − 18 = 8a
a = 18
Hence, the length is 18 metres.

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