EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Pythagoras Theorem
Grade : ICSE Grade IX
License : Non Commercial Use
Question
1
1.
In a right angled triangle △PQR, if QR = 18 cm, PQ = 10 cm are the lengths of perpendicular sides , then perimeter of the triangle =
(i)
51.59 cm
(ii)
53.59 cm
(iii)
48.59 cm
(iv)
45.59 cm
(v)
43.59 cm
Question
2
2.
In the given figure, △DFE is right-angled at F, FG ⟂ DE.
DE
= c,
FE
= a,
DF
= b and
FG
= p.
Which of the following are true?
a)
1
a
2
+
1
b
2
=
1
p
2
b)
ab
=
pc
c)
a
2
+
b
2
=
c
2
d)
1
a
2
+
1
b
2
=
1
c
2
+
1
p
2
e)
1
a
2
+
1
b
2
+
1
c
2
=
1
p
2
(i)
{d,a}
(ii)
{d,e,c}
(iii)
{e,b}
(iv)
{a,b,c}
(v)
{d,a,b}
Question
3
3.
In an isosceles right angled triangle △PQR, if perimeter = 47.8 cm, then side RP =
(i)
16.80 cm
(ii)
22.80 cm
(iii)
24.80 cm
(iv)
19.80 cm
(v)
14.80 cm
Question
4
4.
In the given figure, in △BCD, 'O' is a point inside the triangle. OE ⟂ CD, OF ⟂ BD and OG ⟂ BC. Then
(i)
BG
2
+
CE
2
+
DF
2
=
OB
2
+
OC
2
+
OD
2
−
OE
2
−
OF
2
−
OG
2
(ii)
BG
2
+
CE
2
+
DF
2
=
BC
2
+
ED
2
+
DB
2
−
CG
2
−
DE
2
−
FB
2
(iii)
BG
2
+
CE
2
+
DF
2
=
OB
2
+
OC
2
+
OD
2
+
OE
2
+
OF
2
+
OG
2
(iv)
BG
2
+
CE
2
+
DF
2
=
OG
2
+
OF
2
+
OE
2
Question
5
5.
In a right angled triangle △PQR, if the area is 78 sq.cm and corresponding height of side QR = 12 cm, then side PQ =
(i)
15.00 cm
(ii)
12.00 cm
(iii)
17.00 cm
(iv)
7.00 cm
(v)
9.00 cm
Question
6
6.
In a right angled triangle, if the two non-hypotenuse sides are 16 cm and 63 cm, find the hypotenuse
(i)
66.00 cm
(ii)
64.00 cm
(iii)
65.00 cm
(iv)
63.00 cm
(v)
67.00 cm
Question
7
7.
In the given figure, △DEF is isosceles with DE = DF and EG ⟂ DF. Then
(i)
EG
2
+
DG
2
= 2
FG
.
DG
(ii)
EG
2
−
DG
2
= 2
FG
.
DG
(iii)
EG
2
+
FG
2
= 2
FG
.
DG
(iv)
EG
2
−
FG
2
= 2
FG
.
DG
Question
8
8.
In the given figure, in △CDE, 'O' is a point inside the triangle. OF ⟂ DE, OG ⟂ CE and OH ⟂ CD. Then
(i)
CH
2
+
DF
2
+
EG
2
=
CG
2
+
EF
2
+
DH
2
(ii)
CH
2
+
DF
2
+
EG
2
=
OH
.
OF
+
OF
.
OG
+
OG
.
OH
(iii)
CH
2
+
DF
2
+
EG
2
=
OF
2
+
OG
2
+
OH
2
(iv)
CH
2
+
DF
2
+
EG
2
=
OC
.
OD
+
OD
.
OE
+
OE
.
OC
Question
9
9.
In an isosceles right angled triangle △PQR, if area = 60.5 sq.cm, then corresponding height of side RP =
(i)
9.78 cm
(ii)
5.78 cm
(iii)
6.78 cm
(iv)
7.78 cm
(v)
8.78 cm
Question
10
10.
In an isosceles right angled triangle △PQR, if QR = 17 cm is one of the equal sides, then side RP =
(i)
19.04 cm
(ii)
21.04 cm
(iii)
24.04 cm
(iv)
27.04 cm
(v)
29.04 cm
Question
11
11.
In the given figure, DEFG is a rhombus. Which of the following are true?
a)
EF
2
+
FG
2
=
EG
2
b)
2
DE
2
=
DF
2
+
EG
2
c)
DE
2
+
EF
2
+
FG
2
+
DG
2
=
DF
2
+
EG
2
d)
DE
2
+
EF
2
=
DF
2
e)
4
DE
2
=
DF
2
+
EG
2
(i)
{a,c}
(ii)
{d,a,c}
(iii)
{b,e}
(iv)
{c,e}
(v)
{b,e,c}
Question
12
12.
In a right angled triangle △PQR, if QR = 16 cm is one of the perpendicular sides and RP = 19.42 cm is the hypotenuse, then corresponding height of side QR =
(i)
14.00 cm
(ii)
8.00 cm
(iii)
6.00 cm
(iv)
16.00 cm
(v)
11.00 cm
Question
13
13.
In a right angled triangle △PQR, if the area is 123.5 sq.cm and base QR = 13 cm, then side PQ =
(i)
19.00 cm
(ii)
22.00 cm
(iii)
14.00 cm
(iv)
16.00 cm
(v)
24.00 cm
Question
14
14.
In an isosceles right angled triangle △PQR, if RP = 28.28 cm is the hypotenuse, then side PQ =
(i)
15.00 cm
(ii)
20.00 cm
(iii)
17.00 cm
(iv)
25.00 cm
(v)
23.00 cm
Question
15
15.
In an isosceles right angled triangle △PQR, if QR = 13 cm is one of the equal sides, then area of the triangle =
(i)
89.50 sq.cm
(ii)
87.50 sq.cm
(iii)
84.50 sq.cm
(iv)
79.50 sq.cm
(v)
81.50 sq.cm
Question
16
16.
In the given figure, △BCD is a triangle with BE being the median of CD. Then
(i)
BC
2
+
BD
2
=
CD
2
(ii)
BC
2
+
BD
2
=
2
CE
2
+
2
BE
2
(iii)
BC
2
+
BD
2
=
BE
2
(iv)
BC
2
+
BD
2
=
2
ED
2
+
2
BE
2
(v)
BC
2
+
BD
2
=
2
CE
2
+
2
ED
2
Question
17
17.
In a right angled triangle △PQR, if the base QR = 16 cm and the corresponding height is 19 cm, then perimeter of the triangle =
(i)
59.84 cm
(ii)
54.84 cm
(iii)
56.84 cm
(iv)
64.84 cm
(v)
62.84 cm
Question
18
18.
In an isosceles right angled triangle △PQR, if corresponding height to the base QR is 10 cm, then perimeter of the triangle =
(i)
34.14 cm
(ii)
31.14 cm
(iii)
29.14 cm
(iv)
37.14 cm
(v)
39.14 cm
Question
19
19.
In an isosceles right angled triangle △PQR, if corresponding height to the base QR is 15 cm, then side PQ =
(i)
12.00 cm
(ii)
10.00 cm
(iii)
18.00 cm
(iv)
20.00 cm
(v)
15.00 cm
Question
20
20.
In the given figure, △DEF, DG ⟂ EF. Which of the following are true?
a)
DE
2
+
EG
2
=
DF
2
+
FG
2
b)
DE
2
+
DF
2
=
EG
2
+
FG
2
c)
DG
2
=
2
EG
.
FG
d)
DE
2
−
EG
2
=
DF
2
−
FG
2
e)
DE
2
−
DF
2
=
EG
2
−
FG
2
(i)
{c,a,d}
(ii)
{d,e}
(iii)
{b,e}
(iv)
{b,e,d}
(v)
{a,d}
Question
21
21.
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
=
4
GH
2
+
FH
2
b)
4 (
FQ
2
+
GP
2
) =
5
FG
2
c)
4
FQ
2
=
4
FH
2
+
GH
2
d)
4
GP
2
=
4
GH
2
+
FH
2
e)
4
GP
2
=
4
FH
2
+
GH
2
(i)
{a,b}
(ii)
{a,e,d}
(iii)
{e,c}
(iv)
{a,b,c}
(v)
{b,c,d}
Question
22
22.
In a right angled triangle △PQR, if QR = 16 cm is one of the perpendicular sides and RP = 18.87 cm is the hypotenuse, then area of the triangle =
(i)
77.00 sq.cm
(ii)
83.00 sq.cm
(iii)
75.00 sq.cm
(iv)
85.00 sq.cm
(v)
80.00 sq.cm
Question
23
23.
In an isosceles right angled triangle △PQR, if corresponding height to the base QR is 11 cm, then corresponding height of side PQ =
(i)
16.00 cm
(ii)
11.00 cm
(iii)
6.00 cm
(iv)
8.00 cm
(v)
14.00 cm
Question
24
24.
In a right angled triangle △PQR, if the area is 190 sq.cm and base QR = 19 cm, then perimeter of the triangle =
(i)
71.59 cm
(ii)
63.59 cm
(iii)
61.59 cm
(iv)
66.59 cm
(v)
69.59 cm
Question
25
25.
In a right angled triangle, if one of the sides is 18 cm and hypotenuse 82 cm, find the third side
(i)
82.00 cm
(ii)
79.00 cm
(iii)
81.00 cm
(iv)
80.00 cm
(v)
78.00 cm
Assignment Key
1) (iii)
2) (iv)
3) (iv)
4) (i)
5) (ii)
6) (iii)
7) (iv)
8) (i)
9) (iv)
10) (iii)
11) (iv)
12) (v)
13) (i)
14) (ii)
15) (iii)
16) (ii)
17) (i)
18) (i)
19) (v)
20) (ii)
21) (v)
22) (v)
23) (ii)
24) (iv)
25) (iv)
