ICSE Board Practice

Class VI Class VII Class VIII Class IX Class X
ICSE Grade IX - Pythagoras Theorem
Question 1
1.
    • In the given figure, △EGF is right-angled at G, GH ⟂ EF.
    • EF
    • = c,
    • GF
    • = a,
    • EG
    • = b and
    • GH
    • = p.
    • Which of the following are true?
a)
    • 1
      a
      2
    • +
    • 1
      b
      2
    • =
    • 1
      p
      2
b)
    • 1
      a
      2
    • +
    • 1
      b
      2
    • =
    • 1
      c
      2
    • +
    • 1
      p
      2
c)
    • a
      2
    • +
    • b
      2
    • =
    • c
      2
d)
    • 1
      a
      2
    • +
    • 1
      b
      2
    • +
    • 1
      c
      2
    • =
    • 1
      p
      2
e)
    • ab
    • =
    • pc
  • {a,c,e}
  • {b,d,e}
  • {b,a,c}
  • {d,c}
  • {b,a}
Question 2
2.
In an isosceles right angled triangle △PQR, if RP = 28.28 cm is the hypotenuse, then area of the triangle =
  • 208.00 sq.cm
  • 185.00 sq.cm
  • 184.00 sq.cm
  • 224.00 sq.cm
  • 200.00 sq.cm
Question 3
3.
In an isosceles right angled triangle △PQR, if corresponding height to the base QR is 20 cm, then corresponding height of side PQ =
  • 17.00 cm
  • 15.00 cm
  • 20.00 cm
  • 23.00 cm
  • 25.00 cm
Question 4
4.
A ladder reaches a window which is 8 m above the ground on one side of a street. Keeping its foot at the same point, the ladder is turned to the other side of the street to reach a window 14 m high. Find the width of the street if the length of the ladder is 17 m
  • 23.64 m
  • 24.64 m
  • 22.64 m
  • 25.64 m
  • 26.64 m
Question 5
5.
In a right angled triangle △PQR, if QR = 11 cm, PQ = 15 cm are the lengths of perpendicular sides , then side RP =
  • 23.60 cm
  • 21.60 cm
  • 15.60 cm
  • 13.60 cm
  • 18.60 cm
Question 6
6.
In a right angled triangle △PQR, if QR = 13 cm, PQ = 19 cm are the lengths of perpendicular sides , then area of the triangle =
  • 98.50 sq.cm
  • 119.50 sq.cm
  • 126.50 sq.cm
  • 123.50 sq.cm
  • 140.50 sq.cm
Question 7
7.
In an isosceles right angled triangle △PQR, if RP = 16.97 cm is the hypotenuse, then perimeter of the triangle =
  • 40.97 cm
  • 43.97 cm
  • 45.97 cm
  • 35.97 cm
  • 37.97 cm
Question 8
8.
In a right angled triangle △PQR, if QR = 16 cm is one of the perpendicular sides and RP = 20.62 cm is the hypotenuse, then area of the triangle =
  • 122.00 sq.cm
  • 101.00 sq.cm
  • 108.00 sq.cm
  • 104.00 sq.cm
  • 89.00 sq.cm
Question 9
9.
In a right angled triangle, if one of the sides is 18 cm and hypotenuse 82 cm, find the third side
  • 78.00 cm
  • 82.00 cm
  • 81.00 cm
  • 80.00 cm
  • 79.00 cm
Question 10
10.
    • In the given figure,
    • △FHG
    • is right-angled at
    • H
    • .
    • P
    • is the mid-point of
    • FH
    • and
    • Q
    • is the mid-point of
    • GH
    • .
    • Which of the following cases are true?
a)
    • 4 (
    • FQ
      2
    • +
    • GP
      2
    • ) =
    • 5
    • FG
      2
b)
    • 4
    • FQ
      2
    • =
    • 4
    • FH
      2
    • +
    • GH
      2
c)
    • 4
    • FQ
      2
    • =
    • 4
    • GH
      2
    • +
    • FH
      2
d)
    • 4
    • GP
      2
    • =
    • 4
    • FH
      2
    • +
    • GH
      2
e)
    • 4
    • GP
      2
    • =
    • 4
    • GH
      2
    • +
    • FH
      2
  • {c,d,e}
  • {d,b}
  • {c,a,b}
  • {c,a}
  • {a,b,e}