If a and b are the lengths of the sides of a right triangle whos

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 Multiple Choice QuestionsMultiple Choice Questions

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
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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

213 Views

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

236 Views

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

195 Views

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


B.

180

h2 = a2 + b2 = 102 = 100
Area of Δ ABC = 20 (given)

   Area space of space increment ABC space equals space 1 half space cross times space Base space cross times space Height
  Area of Δ ABC = 1 half space cross times space straight a space cross times space straight b space equals space 20
rightwards double arrow space space straight a space space cross times space space straight b space equals space 40
Now,
 (a + b)2 = a2 + b2  + 2ab
              = 100 + 2 x 40 = 180
                      
   
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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.
242 Views

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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