ICSE Board Practice

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ICSE Grade IX - Pythagoras Theorem
Question 1
1.
In a right angled triangle △PQR, if QR = 13 cm, PQ = 15 cm are the lengths of perpendicular sides , then corresponding height of side PQ =
  • 16.00 cm
  • 10.00 cm
  • 13.00 cm
  • 8.00 cm
  • 18.00 cm
Question 2
2.
In a right angled triangle △PQR, if QR = 20 cm is one of the perpendicular sides and RP = 22.36 cm is the hypotenuse, then perimeter of the triangle =
  • 52.36 cm
  • 57.36 cm
  • 55.36 cm
  • 47.36 cm
  • 49.36 cm
Question 3
3.
In the given figure, in △ABC, 'O' is a point inside the triangle. OD ⟂ BC, OE ⟂ AC and OF ⟂ AB. Then
      • AF
        2
      • +
      • BD
        2
      • +
      • CE
        2
      • =
      • OA
        2
      • +
      • OB
        2
      • +
      • OC
        2
      • +
      • OD
        2
      • +
      • OE
        2
      • +
      • OF
        2
      • AF
        2
      • +
      • BD
        2
      • +
      • CE
        2
      • =
      • OA
        2
      • +
      • OB
        2
      • +
      • OC
        2
      • −
      • OD
        2
      • −
      • OE
        2
      • −
      • OF
        2
      • AF
        2
      • +
      • BD
        2
      • +
      • CE
        2
      • =
      • OF
        2
      • +
      • OE
        2
      • +
      • OD
        2
      • AF
        2
      • +
      • BD
        2
      • +
      • CE
        2
      • =
      • AB
        2
      • +
      • DC
        2
      • +
      • CA
        2
      • −
      • BF
        2
      • −
      • CD
        2
      • −
      • EA
        2
Question 4
4.
In an isosceles right angled triangle △PQR, if corresponding height to the base QR is 18 cm, then corresponding height of side QR =
  • 18.00 cm
  • 21.00 cm
  • 15.00 cm
  • 13.00 cm
  • 23.00 cm
Question 5
5.
In an isosceles right angled triangle △PQR, if corresponding height to the base QR is 10 cm, then side RP =
  • 14.14 cm
  • 19.14 cm
  • 9.14 cm
  • 17.14 cm
  • 11.14 cm
Question 6
6.
In an isosceles right angled triangle △PQR, if corresponding height to the base QR is 15 cm, then corresponding height of side PQ =
  • 12.00 cm
  • 20.00 cm
  • 15.00 cm
  • 10.00 cm
  • 18.00 cm
Question 7
7.
In a right angled triangle △PQR, if QR = 14 cm is one of the perpendicular sides and RP = 17.8 cm is the hypotenuse, then side PQ =
  • 16.00 cm
  • 11.00 cm
  • 6.00 cm
  • 14.00 cm
  • 8.00 cm
Question 8
8.
The altitude and area of an equilateral triangle of side 'a' is
      • 1
        2

        √

        3
      • a,
      		•
        1
        2

        √

        3
      • a
        2

      • √

        3
      • a,
      		•
        1
        2

        √

        3
      • a
      • 1
        2

        √

        3
      • a,
      		•
        1
        4

        √

        3
      • a
        2

      • √

        3
      • a,
      		•
        1
        2

        √

        3
      • a
        2
Question 9
9.
In an isosceles right angled triangle △PQR, if RP = 24.04 cm is the hypotenuse, then perimeter of the triangle =
  • 61.04 cm
  • 58.04 cm
  • 63.04 cm
  • 53.04 cm
  • 55.04 cm
Question 10
10.
In an isosceles right angled triangle △PQR, if QR = 16 cm is one of the equal sides, then corresponding height of side RP =
  • 8.31 cm
  • 6.31 cm
  • 14.31 cm
  • 16.31 cm
  • 11.31 cm