Arithmatical - Area

DIRECTIONS : Problems based on Area.
9. A rectangular plot measuring 90 metres by 50 metres is to be enclosed by wire fencing. If the poles of the fence are kept 5 metres apart, how many poles will be needed?
  A.  55
  B.  56
  C.  57
  D.  58
Solution
Perimeter of the plot = 2 ( 90 + 50 )
= 280 m.
Number of poles = (280 / 5)
= 56 m.
10. The length of a rectangle is twice its breadth. If its length is decreased by 5 cm and breadth is increased by 5 cm, the area of the rectangle is increased by 75 sq.cm. Find the length of the rectangle?
  A.  10 cm
  B.  20 cm
  C.  30 cm
  D.  40 cm
Solution
Let the breadth = x Then length =2x
= [(2x-5)(x+5)-2x ] x [x=75]
x =20.
Length of the rectangle=20cm.

11. A room 5m 55cm long and 3m 74cm broad is to be paved with square tiles. Find the least number of square tiles required to cover the floor?
  A.  176
  B.  175
  C.  185
  D.  188
Solution
Area of the room = (544 x 374)cm ²
Size of largest square tile = H.C.F of 544 & 374cm
= 34 cm
Area of 1 tile = (34 x 34)cm²
Number of tiles required = [544 x 374 / 34 x 34]
= 176.
12. The base of a parallelogram is twice its height. If the area of the parallelogram is 72 sq.cm. Find its height?
  A.  3 cm
  B.  6 cm
  C.  7 cm
  D.  9 cm
Solution
Let the height of the parallelogram be x cm.Then base
= (2x) cm
=2x² = 72
x²=36
x = 6.
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