EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Pythagoras Theorem
Grade : ICSE Grade IX
License : Non Commercial Use
Question
1
1.
In an isosceles right angled triangle △PQR, if QR = 14 cm is one of the equal sides, then area of the triangle =
(i)
93.00 sq.cm
(ii)
98.00 sq.cm
(iii)
95.00 sq.cm
(iv)
101.00 sq.cm
(v)
103.00 sq.cm
Question
2
2.
In the given figure, △EFG is an obtuse angled triangle and EH ⟂ FG. Then
(i)
EG
2
=
EF
2
+
FG
2
+
2
FG
.
FH
(ii)
EG
2
=
EF
2
+
FG
2
+
FH
2
(iii)
EG
2
=
EF
2
+
FG
2
−
2
FG
.
FH
(iv)
EG
2
=
EF
2
+
FG
2
+
2
FH
.
GH
(v)
EG
2
=
EF
2
+
FG
2
+
2
EF
.
FG
Question
3
3.
A vehicle goes 11 km West and then 13 km North. How far is it from its starting point ?
(i)
16.03 km
(ii)
15.03 km
(iii)
18.03 km
(iv)
19.03 km
(v)
17.03 km
Question
4
4.
In an isosceles right angled triangle △PQR, if area = 162 sq.cm, then perimeter of the triangle =
(i)
66.46 cm
(ii)
64.46 cm
(iii)
61.46 cm
(iv)
56.46 cm
(v)
58.46 cm
Question
5
5.
In a right angled triangle △PQR, if QR = 20 cm, PQ = 11 cm are the lengths of perpendicular sides , then corresponding height of side QR =
(i)
16.00 cm
(ii)
6.00 cm
(iii)
14.00 cm
(iv)
11.00 cm
(v)
8.00 cm
Question
6
6.
In an isosceles right angled triangle △PQR, if corresponding height to the base QR is 20 cm, then perimeter of the triangle =
(i)
71.28 cm
(ii)
68.28 cm
(iii)
73.28 cm
(iv)
63.28 cm
(v)
65.28 cm
Question
7
7.
In a right angled triangle △PQR, if the area is 65 sq.cm and corresponding height of side QR = 10 cm, then side QR =
(i)
8.00 cm
(ii)
13.00 cm
(iii)
18.00 cm
(iv)
16.00 cm
(v)
10.00 cm
Question
8
8.
In an isosceles right angled triangle △PQR, if area = 162 sq.cm, then corresponding height of side QR =
(i)
23.00 cm
(ii)
13.00 cm
(iii)
15.00 cm
(iv)
21.00 cm
(v)
18.00 cm
Question
9
9.
In an isosceles right angled triangle △PQR, if RP = 16.97 cm is the hypotenuse, then corresponding height of side PQ =
(i)
9.00 cm
(ii)
12.00 cm
(iii)
17.00 cm
(iv)
15.00 cm
(v)
7.00 cm
Question
10
10.
In a right angled triangle △PQR, if the area is 88 sq.cm and base QR = 11 cm, then corresponding height of side PQ =
(i)
8.00 cm
(ii)
11.00 cm
(iii)
16.00 cm
(iv)
14.00 cm
(v)
6.00 cm
Question
11
11.
In a right angled triangle △PQR, if QR = 14 cm is one of the perpendicular sides and RP = 21.26 cm is the hypotenuse, then corresponding height of side QR =
(i)
13.00 cm
(ii)
16.00 cm
(iii)
11.00 cm
(iv)
19.00 cm
(v)
21.00 cm
Question
12
12.
In the given figure, △CDE, CF ⟂ DE. Which of the following are true?
a)
CD
2
+
CE
2
=
DF
2
+
EF
2
b)
CF
2
=
2
DF
.
EF
c)
CD
2
+
DF
2
=
CE
2
+
EF
2
d)
CD
2
−
DF
2
=
CE
2
−
EF
2
e)
CD
2
−
CE
2
=
DF
2
−
EF
2
(i)
{d,e}
(ii)
{b,e,d}
(iii)
{a,d}
(iv)
{b,e}
(v)
{c,a,d}
Question
13
13.
In an isosceles right angled triangle △PQR, if area = 144.5 sq.cm, then corresponding height of side RP =
(i)
7.02 cm
(ii)
9.02 cm
(iii)
17.02 cm
(iv)
12.02 cm
(v)
15.02 cm
Question
14
14.
In the given figure, △GHI is a triangle in which GH = GI and J is a point on HI. Then
(i)
GH
2
−
GJ
2
=
HJ
.
IJ
(ii)
GH
2
−
GJ
2
=
GJ
.
HJ
(iii)
GH
2
+
GJ
2
=
HI
2
(iv)
GH
2
−
GJ
2
=
GJ
.
IJ
(v)
GH
2
+
GJ
2
=
HJ
.
IJ
Question
15
15.
In a right angled triangle △PQR, if the area is 104.5 sq.cm and base QR = 11 cm, then side PQ =
(i)
24.00 cm
(ii)
14.00 cm
(iii)
16.00 cm
(iv)
22.00 cm
(v)
19.00 cm
Question
16
16.
In a right angled triangle △PQR, if QR = 13 cm is one of the perpendicular sides and RP = 19.85 cm is the hypotenuse, then area of the triangle =
(i)
100.50 sq.cm
(ii)
102.50 sq.cm
(iii)
94.50 sq.cm
(iv)
92.50 sq.cm
(v)
97.50 sq.cm
Question
17
17.
In a right angled triangle △PQR, if the base QR = 14 cm and the corresponding height is 13 cm, then side RP =
(i)
14.10 cm
(ii)
16.10 cm
(iii)
19.10 cm
(iv)
24.10 cm
(v)
22.10 cm
Question
18
18.
In a right angled triangle △PQR, if the area is 120 sq.cm and base QR = 16 cm, then perimeter of the triangle =
(i)
57.93 cm
(ii)
52.93 cm
(iii)
49.93 cm
(iv)
55.93 cm
(v)
47.93 cm
Question
19
19.
In a right angled triangle △PQR, if QR = 13 cm is one of the perpendicular sides and RP = 20.62 cm is the hypotenuse, then perimeter of the triangle =
(i)
52.62 cm
(ii)
49.62 cm
(iii)
44.62 cm
(iv)
46.62 cm
(v)
54.62 cm
Question
20
20.
In the given figure, △ABC is an acute angled triangle and AD ⟂ BC. Then
(i)
AC
2
=
AB
2
+
BC
2
−
2
BC
.
BD
(ii)
AC
2
=
AB
2
+
BC
2
−
2
AB
.
BC
(iii)
AC
2
=
AB
2
+
BC
2
+
2
BC
.
BD
(iv)
AC
2
=
AB
2
+
BC
2
−
AD
2
(v)
AC
2
=
AB
2
+
BC
2
+
2
AB
.
BC
Question
21
21.
In an isosceles right angled triangle △PQR, if corresponding height to the base QR is 12 cm, then side QR =
(i)
12.00 cm
(ii)
15.00 cm
(iii)
7.00 cm
(iv)
17.00 cm
(v)
9.00 cm
Question
22
22.
In a right angled triangle, if the two non-hypotenuse sides are 20 cm and 99 cm, find the hypotenuse
(i)
99.00 cm
(ii)
102.00 cm
(iii)
101.00 cm
(iv)
100.00 cm
(v)
103.00 cm
Question
23
23.
In a right angled triangle △PQR, if the base QR = 16 cm and the corresponding height is 12 cm, then corresponding height of side PQ =
(i)
11.00 cm
(ii)
13.00 cm
(iii)
19.00 cm
(iv)
16.00 cm
(v)
21.00 cm
Question
24
24.
In an isosceles right angled triangle △PQR, if perimeter = 34.14 cm, then side RP =
(i)
14.14 cm
(ii)
17.14 cm
(iii)
9.14 cm
(iv)
11.14 cm
(v)
19.14 cm
Question
25
25.
In an equilateral triangle ABC, the side BC is trisected at D. Then
(i)
7 AD
2
=
3 AB
2
(ii)
9 AD
2
=
7 AB
2
(iii)
3 AD
2
=
7 AB
2
(iv)
7 AD
2
=
9 AB
2
Assignment Key
1) (ii)
2) (i)
3) (v)
4) (iii)
5) (iv)
6) (ii)
7) (ii)
8) (v)
9) (ii)
10) (ii)
11) (ii)
12) (i)
13) (iv)
14) (i)
15) (v)
16) (v)
17) (iii)
18) (ii)
19) (ii)
20) (i)
21) (i)
22) (iii)
23) (iv)
24) (i)
25) (ii)
