ICSE Board Practice

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ICSE Grade IX - Pythagoras Theorem
Question 1
1.
In a right angled triangle △PQR, if the base QR = 20 cm and the corresponding height is 14 cm, then side PQ =
  • 14.00 cm
  • 19.00 cm
  • 9.00 cm
  • 11.00 cm
  • 17.00 cm
Question 2
2.
In a right angled triangle △PQR, if QR = 14 cm, PQ = 20 cm are the lengths of perpendicular sides , then area of the triangle =
  • 128.00 sq.cm
  • 124.00 sq.cm
  • 140.00 sq.cm
  • 164.00 sq.cm
  • 143.00 sq.cm
Question 3
3.
In a right angled triangle △PQR, if QR = 16 cm, PQ = 11 cm are the lengths of perpendicular sides , then side RP =
  • 22.42 cm
  • 14.42 cm
  • 19.42 cm
  • 16.42 cm
  • 24.42 cm
Question 4
4.
In a right angled triangle △PQR, if QR = 15 cm is one of the perpendicular sides and RP = 19.85 cm is the hypotenuse, then corresponding height of side PQ =
  • 15.00 cm
  • 18.00 cm
  • 10.00 cm
  • 12.00 cm
  • 20.00 cm
Question 5
5.
In the given figure, CDEF is a rhombus. Which of the following are true?
a)
    • 2
    • CD
      2
    • =
    • CE
      2
    • +
    • DF
      2
b)
    • 4
    • CD
      2
    • =
    • CE
      2
    • +
    • DF
      2
c)
    • CD
      2
    • +
    • DE
      2
    • +
    • EF
      2
    • +
    • CF
      2
    • =
    • CE
      2
    • +
    • DF
      2
d)
    • DE
      2
    • +
    • EF
      2
    • =
    • DF
      2
e)
    • CD
      2
    • +
    • DE
      2
    • =
    • CE
      2
  • {d,c,b}
  • {b,c}
  • {e,a,b}
  • {d,c}
  • {a,b}
Question 6
6.
In a right angled triangle, if the two non-hypotenuse sides are 18 cm and 80 cm, find the hypotenuse
  • 83.00 cm
  • 84.00 cm
  • 81.00 cm
  • 82.00 cm
  • 80.00 cm
Question 7
7.
In a right angled triangle △PQR, if the base QR = 11 cm and the corresponding height is 20 cm, then corresponding height of side RP =
  • 7.64 cm
  • 10.64 cm
  • 9.64 cm
  • 11.64 cm
  • 8.64 cm
Question 8
8.
In a right angled triangle △PQR, if the area is 112 sq.cm and corresponding height of side QR = 16 cm, then corresponding height of side PQ =
  • 14.00 cm
  • 9.00 cm
  • 11.00 cm
  • 17.00 cm
  • 19.00 cm
Question 9
9.
In the given figure, △EFG is isosceles with EF = EG and FH ⟂ EG. Then
      • FH
        2
      • +
      • GH
        2
      • = 2
      • GH
      • .
      • EH
      • FH
        2
      • +
      • EH
        2
      • = 2
      • GH
      • .
      • EH
      • FH
        2
      • −
      • EH
        2
      • = 2
      • GH
      • .
      • EH
      • FH
        2
      • −
      • GH
        2
      • = 2
      • GH
      • .
      • EH
Question 10
10.
In an equilateral triangle ABC, the side BC is trisected at D. Then
      • 3 AD
        2
      • =
      • 7 AB
        2
      • 7 AD
        2
      • =
      • 3 AB
        2
      • 9 AD
        2
      • =
      • 7 AB
        2
      • 7 AD
        2
      • =
      • 9 AB
        2