One of the angles of a right-angled is 15°, and the hypotenuse

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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

202 Views

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


C.

1250



Area of triangle  =  1 half cross times straight B cross times straight P
Base space of space triangle space space equals space cos space 15 space degree space equals space straight B over straight H
cos space 15 degree space equals space cos thin space left parenthesis 45 degree space minus space 30 degree right parenthesis
       equals space cos space 45 degree. space cos space 30 degree space plus space sin space 45 degree. space sin space 30 degree
equals space fraction numerator 1 over denominator square root of 2 end fraction cross times space fraction numerator square root of 3 over denominator 2 end fraction space plus space fraction numerator 1 over denominator square root of 2 end fraction space cross times space 1 half space equals space fraction numerator square root of 3 plus 1 over denominator 2 square root of 2 end fraction
 
Perpendicular of triangle  = sin space 15 degree space equals space straight P over straight H
   sin space 15 degree space equals space sin space left parenthesis 45 degree space minus space 30 degree right parenthesis
space equals space sin space 45 degree space cross times space cos space 30 degree space minus space cos space 45 degree space cross times space sin space 30 degree
equals space fraction numerator 1 over denominator square root of 2 end fraction cross times fraction numerator square root of 3 over denominator 2 end fraction space minus space fraction numerator 1 over denominator square root of 2 end fraction cross times space 1 half space equals space fraction numerator square root of 3 minus 1 over denominator 2 square root of 2 end fraction
Now, Area of triangle  equals space 1 half cross times open parentheses fraction numerator square root of 3 begin display style minus end style begin display style 1 end style over denominator 2 square root of 2 end fraction cross times fraction numerator square root of 3 begin display style minus end style begin display style 1 end style over denominator 2 square root of 2 end fraction close parentheses
                        equals space 1 half space cross times space fraction numerator left parenthesis 3 minus 1 right parenthesis over denominator 8 end fraction space equals space 1 over 8 space cm squared
equals space 1 over 8 space cross times space 10000 space equals space 1250 space cm squared



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