The area of the parallelogram whose length is 30 cm, width is 20

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31.

The area of the parallelogram whose length is 30 cm, width is 20 cm and one diagonal is 40 cm is

  • 200 square root of 15 space cm squared
  • 100 square root of 15 space cm squared
  • 300 square root of 15 space cm squared
  • 300 square root of 15 space cm squared


D.

300 square root of 15 space cm squared



In ΔABD, AB = 20 cm, AD = 30 cm, BD (Diagonal) = 40 cm
therefore space space space Semi minus Perimeter space left parenthesis straight s right parenthesis space equals space fraction numerator straight a plus straight b plus straight c over denominator 2 end fraction space equals space fraction numerator 20 plus 30 plus 40 over denominator 2 end fraction space equals space 45 space cm
∴ Area of Δ ABD
       equals space square root of straight s left parenthesis straight s minus straight a right parenthesis thin space left parenthesis straight s minus straight b right parenthesis thin space left parenthesis straight s minus straight c right parenthesis end root
equals space square root of 45 left parenthesis 45 minus 20 right parenthesis thin space left parenthesis 45 minus 30 right parenthesis thin space left parenthesis 45 minus 40 right parenthesis end root
equals square root of 45 space cross times space 25 space cross times space 15 space cross times space 5 end root
       equals square root of 5 space cross times 3 cross times 3 cross times 5 cross times 5 cross times 5 cross times 3 cross times 5 end root
equals square root of 5 squared space cross times space 5 squared space cross times space 5 space cross times space 3 squared space cross times space 3 end root
equals space 5 space cross times space 5 space cross times space 3 square root of 15 space equals space 75 square root of 15 space cm squared

∴   Area of parallelogram ABCD = 2 space cross times space 75 square root of 15
         equals space 150 square root of 15 space cm squared

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32.

On increasing each side of a square by 50%, the ratio of the area of new square formed and the given square will be

  • 9 : 5

  • 9 : 3.5

  • 9 : 7

  • 9 : 7

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33.

The area of circle is 324 space straight pi square cm. The length of its longest chord (in cm) is

  • 36

  • 28

  • 38

  • 38

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34.

The area of a rhombus is 256 square cm and one of its diagonals is twice the other in length. Then length of its largest diagonal is

  • 32 cm

  • 16 cm

  • 48 cm

  • 48 cm

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35.

If the side of a square is 1 half left parenthesis straight x plus 1 right parenthesis space units and its diagonal is fraction numerator 3 minus straight x over denominator square root of 2 end fraction units comma then the length of the side of the square would be

  • 4 over 3 space units
  • 1 half space unit
  • 1 unit

  • 1 unit

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36.

For an equilateral triangle, the ratio of the in-radius and the ex-radius is

  • 1 : 2

  • 1 space colon space square root of 2
  • 1 : 3

  • 1 : 3

231 Views

37.

The circumference of a triangle is 24 cm and the circumference of its in-circle is 44 cm. Then the area of the triangle is (taking straight pi space equals space 22 over 7)

  • 56 square cm.

  • 84 square cm.

  • 48 square cm

  • 48 square cm

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38.

If a and b are the lengths of the sides of a right triangle whose hypotenuse is 10 and whose area is 20, then the value of (a + b)2 is

  • 140

  • 180

  • 120

  • 120

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39.

If the length of each of two equal sides of an isosceles triangle is 10 cm and the adjacent angle is 45°, then the area of the triangle is

  • 20 square root of 2 space square space cm.
  • 12 square root of 2 space square space cm.
  • 25 square root of 2 space square space cm.
  • 25 square root of 2 space square space cm.
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40.

One of the angles of a right-angled is 15°, and the hypotenuse is 1 metre. The area of the triangle (in square cm) is

  • 1220

  • 1200

  • 1250

  • 1250

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