Perimeter of a rhombus is 2p unit and sum of length of diagonals

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41.

In an equilateral triangle of side 24 cm, a circle is inscribed touching its sides. The area of the remaining portion of the triangle is ( √3 = 1.732 )

  • 98.55 sq cm

  • 100 sq cm

  • 101 sq cm

  • 95 sq cm

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42.

Two sides of a plot measuring 32 m and 24 m and the angle between them is a perfect right angle. The other two sides measure 25 m each and the other three angles are not right angles. The area of the plot in m2 is

  • 768

  • 534

  • 696.5

  • 696.5

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43.

Perimeter of a rhombus is 2p unit and sum of length of diagonals is m unit, then area of the rhombus is


C.

Let d1, d2 be the diagonals of the rhombus
Perimeter of rhombus (P) = 2 square root of straight d subscript 1 squared plus straight d subscript 2 squared end root
                         Perimeter = 2p(given)

∴       2 straight p space equals space 2 square root of straight d subscript 1 squared space plus space straight d subscript 2 squared end root
Squaring both the sides, we get
         straight p squared space equals space straight d subscript 1 squared space plus space straight d subscript 2 squared       ...(i)
Now, sum of diagonals (d1 + d2) =  m (given)
  Again, Squaring both the sides, we get
               left parenthesis straight d subscript 1 space plus space straight d subscript 2 right parenthesis squared space equals space straight m squared
         rightwards double arrow space space straight d subscript 1 squared space plus space straight d subscript 2 squared space plus space 2 space cross times space straight d subscript 1 space cross times space straight d subscript 2 space equals space straight m squared
         rightwards double arrow space space space straight p squared space plus space 2. straight d subscript 1. straight d subscript 2 space equals space straight m squared space space space space left square bracket using space left parenthesis straight i right parenthesis right square bracket
rightwards double arrow space space space space space space space space space space 2. space straight d subscript 1. space straight d subscript 2 space equals space straight m squared space minus space straight p squared
rightwards double arrow space space space space space space space space space space space straight d subscript 1. space straight d subscript 2 space equals space fraction numerator straight m squared minus straight p squared over denominator 2 end fraction space.... left parenthesis ii right parenthesis

Area of rhombus = 1 half cross times space straight d subscript 1 space cross times space straight d subscript 2
                        equals space 1 half space cross times space fraction numerator straight m squared minus straight p squared over denominator 2 end fraction space space space left square bracket using space left parenthesis ii right parenthesis right square bracket
equals space 1 fourth left parenthesis straight m squared minus straight p squared right parenthesis
                          
 
         

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44.

The diameter of a circular wheel is 7 m. How many revolutions will it make in travelling 22 km?

  • 100

  • 400

  • 500

  • 500

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45.

The area of an equilateral triangle is 9 square root of 3 space straight m squared. The length (in m) of the median is

  • 2 square root of 3
  • 3 square root of 3
  • 3 square root of 2
  • 3 square root of 2
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46.

The diagonals of a rhombus are 12 cm and 16 cm respectively. The length of one side is

  • 8 cm

  • 6 cm

  • 10 cm

  • 10 cm

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47.

How many tiles, each 4 decimetre square, will be required to cover the floor of a room 8 m long and 6 m broad?

  • 200

  • 260

  • 280

  • 280

277 Views

48.

A lawn is in the form of a rectangle having its breadth and length in the ratio 3 : 4. The area of the lawn is 1 over 12 hectare. The breadth of the lawn is

  • 25 metres

  • 50 metres

  • 75 metres

  • 75 metres

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49.

The area of a rectangle is thrice that of a square. The length of the rectangle is 20 cm and the breadth of the rectangle is 3 over 2 times that of the side of the square. The side of the square, in cm, is

  • 10

  • 20

  • 30

  • 30

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50.

A square is of area 200 sq. m. A new square is formed in such a way that the length of its diagonal is square root of 2 times of the diagonal of the given square. Then the area of the new square formed is

  • 200 square root of 2 space sq. space straight m
  • 400 square root of 2 space sq space. straight m.
  • 400 sq. m.

  • 400 sq. m.

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