ICSE Board Practice

Class VI Class VII Class VIII Class IX Class X
ICSE Grade IX - Pythagoras Theorem
Question 1
1.
In an isosceles right angled triangle △PQR, if area = 72 sq.cm, then side QR =
  • 17.00 cm
  • 12.00 cm
  • 15.00 cm
  • 9.00 cm
  • 7.00 cm
Question 2
2.
In a right angled triangle △PQR, if the area is 104.5 sq.cm and corresponding height of side QR = 11 cm, then corresponding height of side RP =
  • 11.52 cm
  • 10.52 cm
  • 7.52 cm
  • 9.52 cm
  • 8.52 cm
Question 3
3.
In an isosceles right angled triangle △PQR, if area = 162 sq.cm, then side RP =
  • 22.46 cm
  • 28.46 cm
  • 30.46 cm
  • 25.46 cm
  • 20.46 cm
Question 4
4.
In an isosceles right angled triangle △PQR, if RP = 22.63 cm is the hypotenuse, then side QR =
  • 16.00 cm
  • 11.00 cm
  • 19.00 cm
  • 13.00 cm
  • 21.00 cm
Question 5
5.
    • In the given figure,
    • △DFE
    • is right-angled at
    • F
    • .
    • Q
    • is the mid-point of
    • DF
    • and
    • R
    • is the mid-point of
    • EF
    • .
    • Which of the following cases are true?
a)
    • 4
    • EQ
      2
    • =
    • 4
    • EF
      2
    • +
    • DF
      2
b)
    • 4
    • DR
      2
    • =
    • 4
    • EF
      2
    • +
    • DF
      2
c)
    • 4 (
    • DR
      2
    • +
    • EQ
      2
    • ) =
    • 5
    • DE
      2
d)
    • 4
    • DR
      2
    • =
    • 4
    • DF
      2
    • +
    • EF
      2
e)
    • 4
    • EQ
      2
    • =
    • 4
    • DF
      2
    • +
    • EF
      2
  • {a,c,d}
  • {b,a}
  • {b,e,d}
  • {e,c}
  • {b,a,c}
Question 6
6.
In a right angled triangle, if one of the sides is 8 cm and hypotenuse 17 cm, find the third side
  • 14.00 cm
  • 13.00 cm
  • 15.00 cm
  • 16.00 cm
  • 17.00 cm
Question 7
7.
In the given figure, BCDE is a rhombus. Which of the following are true?
a)
    • 4
    • BC
      2
    • =
    • BD
      2
    • +
    • CE
      2
b)
    • 2
    • BC
      2
    • =
    • BD
      2
    • +
    • CE
      2
c)
    • CD
      2
    • +
    • DE
      2
    • =
    • CE
      2
d)
    • BC
      2
    • +
    • CD
      2
    • =
    • BD
      2
e)
    • BC
      2
    • +
    • CD
      2
    • +
    • DE
      2
    • +
    • BE
      2
    • =
    • BD
      2
    • +
    • CE
      2
  • {a,e}
  • {c,e,a}
  • {c,e}
  • {b,a}
  • {d,b,a}
Question 8
8.
In a right angled triangle △PQR, if the area is 120 sq.cm and corresponding height of side QR = 12 cm, then corresponding height of side PQ =
  • 15.00 cm
  • 20.00 cm
  • 25.00 cm
  • 17.00 cm
  • 23.00 cm
Question 9
9.
In a right angled triangle △PQR, if the area is 91 sq.cm and base QR = 14 cm, then perimeter of the triangle =
  • 49.10 cm
  • 43.10 cm
  • 41.10 cm
  • 46.10 cm
  • 51.10 cm
Question 10
10.
In a right angled triangle △PQR, if QR = 14 cm, PQ = 18 cm are the lengths of perpendicular sides , then corresponding height of side PQ =
  • 14.00 cm
  • 19.00 cm
  • 11.00 cm
  • 9.00 cm
  • 17.00 cm