ICSE Board Practice

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ICSE Grade IX - Pythagoras Theorem
Question 1
1.
In a right angled triangle △PQR, if QR = 17 cm is one of the perpendicular sides and RP = 20.81 cm is the hypotenuse, then corresponding height of side RP =
  • 7.80 cm
  • 11.80 cm
  • 9.80 cm
  • 10.80 cm
  • 8.80 cm
Question 2
2.
In the given figure, O is a point in the interior of the rectangle ABCD. Then
      • OA
        2
      • +
      • OC
        2
      • =
      • OB
        2
      • +
      • OD
        2
      • OA
        2
      • +
      • OB
        2
      • +
      • OC
        2
      • +
      • OD
        2
      • =
      • AB
        2
      • +
      • BC
        2
      • +
      • CD
        2
      • +
      • DA
        2
      • OA
        2
      • −
      • OC
        2
      • =
      • OB
        2
      • −
      • OD
        2
      • OA
        2
      • +
      • OB
        2
      • +
      • OC
        2
      • +
      • OD
        2
      • =
      • AC
        2
      • +
      • BD
        2
Question 3
3.
In an isosceles right angled triangle △PQR, if QR = 15 cm is one of the equal sides, then side PQ =
  • 18.00 cm
  • 15.00 cm
  • 20.00 cm
  • 12.00 cm
  • 10.00 cm
Question 4
4.
In a right angled triangle △PQR, if the area is 70 sq.cm and base QR = 14 cm, then side RP =
  • 22.20 cm
  • 14.20 cm
  • 17.20 cm
  • 12.20 cm
  • 20.20 cm
Question 5
5.
    • In the given figure,
    • △CED
    • is right-angled at
    • E
    • .
    • P
    • is the mid-point of
    • CE
    • and
    • Q
    • is the mid-point of
    • DE
    • .
    • Which of the following cases are true?
a)
    • 4
    • CQ
      2
    • =
    • 4
    • DE
      2
    • +
    • CE
      2
b)
    • 4
    • DP
      2
    • =
    • 4
    • CE
      2
    • +
    • DE
      2
c)
    • 4
    • DP
      2
    • =
    • 4
    • DE
      2
    • +
    • CE
      2
d)
    • 4 (
    • CQ
      2
    • +
    • DP
      2
    • ) =
    • 5
    • CD
      2
e)
    • 4
    • CQ
      2
    • =
    • 4
    • CE
      2
    • +
    • DE
      2
  • {a,c,d}
  • {a,c}
  • {b,d}
  • {a,b,e}
  • {c,d,e}
Question 6
6.
In a right angled triangle, if the two non-hypotenuse sides are 12 cm and 35 cm, find the hypotenuse
  • 37.00 cm
  • 38.00 cm
  • 36.00 cm
  • 39.00 cm
  • 35.00 cm
Question 7
7.
In a right angled triangle △PQR, if QR = 20 cm is one of the perpendicular sides and RP = 23.32 cm is the hypotenuse, then side PQ =
  • 17.00 cm
  • 15.00 cm
  • 12.00 cm
  • 7.00 cm
  • 9.00 cm
Question 8
8.
In an isosceles right angled triangle △PQR, if corresponding height to the base QR is 19 cm, then corresponding height of side RP =
  • 10.44 cm
  • 13.44 cm
  • 18.44 cm
  • 16.44 cm
  • 8.44 cm
Question 9
9.
In a right angled triangle △PQR, if QR = 10 cm, PQ = 19 cm are the lengths of perpendicular sides , then perimeter of the triangle =
  • 55.47 cm
  • 53.47 cm
  • 50.47 cm
  • 47.47 cm
  • 45.47 cm
Question 10
10.
In a right angled triangle △PQR, if the base QR = 12 cm and the corresponding height is 16 cm, then perimeter of the triangle =
  • 45.00 cm
  • 53.00 cm
  • 48.00 cm
  • 51.00 cm
  • 43.00 cm