(16) In a four sided field, the longer diagonal is 220 m.  The perpendicular drawn from the opposite vertices to the longer are  49.4 m and 50.6 m. Find the area of  the field.

Soln.

Area =  

=   + 

=   ( 50.6   +   49.4 )

=   11000  m²

↦    1 km²   =   10,00,000  m²

↦    1 m²   =   10,000  cm²

↦    1 hectare   =   10,000  m²

↦    1 are   =  100 m²

(17) The base of a triangular field is four times its altitude. If the cost of  cultivating the field at Rs. 2000 per hectare be Rs. 16000, find its base and height.

Soln. Area of  the field   =     =    hectares.  =   8 × 10000 m²

Let, the height  =  x metres. Then, base  =  4x metres.

× x × 4x  =  80000   ⇒   x²  =  40000   ⇒   x  =  200.

∴ Height  =  200 m  and  Base  =  800 m.2.

 (18) The sides of  a rectangular lawn are in the ratio 3 : 5 and its area is  hectares. Find the dimensions of  the lawn.

Soln. Let the sides  be  3x  and  5x.

Then,    .

  =  20 m    &   Length  = 

(19) Find the cost of  carpeting a room 12 m long and 10 m wide  with a carpet  75 cm broad at Rs. 8 per meter. 

Soln. Let, the length of  a carpet  =  x

Now,  Area of  the carpet   =   Area of  a  room

  x    =    160 m

Now, cost of  the carpet  =  160    8  =   Rs.  1280

(20) A room is 12 m long, 8 m broad and 10 m high. Find the cost of  papering the four walls of  the room at Rs. 10 per m², it being given that doors and windows occupy 50 m².

Soln. Area of  4 walls  =  2 ( length + breadth ) × height

=  [ 2 ( 12 + 8 ) × 10 ]  =  400 m².

Area  to be papered  =  ( 400 – 50 )  =  350 m².

∴ Cost of  papering  =  Rs. ( 350 × 10 )  =  Rs. 3500.

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