ICSE Board Practice

Class VI Class VII Class VIII Class IX Class X
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 area of the triangle =
  • 92.50 sq.cm
  • 97.50 sq.cm
  • 102.50 sq.cm
  • 94.50 sq.cm
  • 100.50 sq.cm
Question 2
2.
In a right angled triangle △PQR, if the base QR = 18 cm and the corresponding height is 20 cm, then side PQ =
  • 23.00 cm
  • 17.00 cm
  • 20.00 cm
  • 25.00 cm
  • 15.00 cm
Question 3
3.
In the given figure, △DEF is a triangle in which DE = DF and G is a point on EF. Then
      • DE
        2
      • −
      • DG
        2
      • =
      • EG
      • .
      • FG
      • DE
        2
      • +
      • DG
        2
      • =
      • EF
        2
      • DE
        2
      • −
      • DG
        2
      • =
      • DG
      • .
      • EG
      • DE
        2
      • −
      • DG
        2
      • =
      • DG
      • .
      • FG
      • DE
        2
      • +
      • DG
        2
      • =
      • EG
      • .
      • FG
Question 4
4.
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 corresponding height of side PQ =
  • 20.00 cm
  • 17.00 cm
  • 23.00 cm
  • 25.00 cm
  • 15.00 cm
Question 5
5.
In an isosceles right angled triangle △PQR, if RP = 26.87 cm is the hypotenuse, then side QR =
  • 22.00 cm
  • 16.00 cm
  • 24.00 cm
  • 19.00 cm
  • 14.00 cm
Question 6
6.
In an isosceles right angled triangle △PQR, if area = 98 sq.cm, then corresponding height of side QR =
  • 9.00 cm
  • 17.00 cm
  • 14.00 cm
  • 19.00 cm
  • 11.00 cm
Question 7
7.
In an isosceles right angled triangle △PQR, if RP = 19.8 cm is the hypotenuse, then area of the triangle =
  • 95.00 sq.cm
  • 103.00 sq.cm
  • 93.00 sq.cm
  • 98.00 sq.cm
  • 101.00 sq.cm
Question 8
8.
    • In the given figure, △ACB is right-angled at C, CD ⟂ AB.
    • AB
    • = c,
    • CB
    • = a,
    • AC
    • = b and
    • CD
    • = p.
    • Which of the following are true?
a)
    • 1
      a
      2
    • +
    • 1
      b
      2
    • +
    • 1
      c
      2
    • =
    • 1
      p
      2
b)
    • ab
    • =
    • pc
c)
    • 1
      a
      2
    • +
    • 1
      b
      2
    • =
    • 1
      c
      2
    • +
    • 1
      p
      2
d)
    • 1
      a
      2
    • +
    • 1
      b
      2
    • =
    • 1
      p
      2
e)
    • a
      2
    • +
    • b
      2
    • =
    • c
      2
  • {a,b,d}
  • {a,b}
  • {a,c,e}
  • {b,d,e}
  • {c,d}
Question 9
9.
In an isosceles right angled triangle △PQR, if RP = 26.87 cm is the hypotenuse, then side PQ =
  • 19.00 cm
  • 22.00 cm
  • 14.00 cm
  • 24.00 cm
  • 16.00 cm
Question 10
10.
In a right angled triangle △PQR, if the area is 105 sq.cm and base QR = 15 cm, then side PQ =
  • 14.00 cm
  • 19.00 cm
  • 17.00 cm
  • 9.00 cm
  • 11.00 cm