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 the area is 130 sq.cm and corresponding height of side QR = 20 cm, then side RP =
(i)
23.85 cm
(ii)
18.85 cm
(iii)
20.85 cm
(iv)
28.85 cm
(v)
26.85 cm
Question
2
2.
In the given figure, CDEF is a rhombus. Which of the following are true?
a)
CD
2
+
DE
2
=
CE
2
b)
CD
2
+
DE
2
+
EF
2
+
CF
2
=
CE
2
+
DF
2
c)
DE
2
+
EF
2
=
DF
2
d)
4
CD
2
=
CE
2
+
DF
2
e)
2
CD
2
=
CE
2
+
DF
2
(i)
{e,a,b}
(ii)
{b,d}
(iii)
{c,d}
(iv)
{c,d,b}
(v)
{a,b}
Question
3
3.
In a right angled triangle △PQR, if QR = 15 cm, PQ = 12 cm are the lengths of perpendicular sides , then perimeter of the triangle =
(i)
49.21 cm
(ii)
46.21 cm
(iii)
41.21 cm
(iv)
51.21 cm
(v)
43.21 cm
Question
4
4.
In an isosceles right angled triangle △PQR, if area = 72 sq.cm, then side RP =
(i)
16.97 cm
(ii)
11.97 cm
(iii)
21.97 cm
(iv)
13.97 cm
(v)
19.97 cm
Question
5
5.
In a right angled triangle △PQR, if the area is 75 sq.cm and base QR = 10 cm, then side PQ =
(i)
18.00 cm
(ii)
10.00 cm
(iii)
15.00 cm
(iv)
20.00 cm
(v)
12.00 cm
Question
6
6.
In the given figure,
△ACB
is right-angled at
C
.
R
is the mid-point of
AC
and
S
is the mid-point of
BC
.
Which of the following cases are true?
a)
4
AS
2
=
4
AC
2
+
BC
2
b)
4
AS
2
=
4
BC
2
+
AC
2
c)
4 (
AS
2
+
BR
2
) =
5
AB
2
d)
4
BR
2
=
4
BC
2
+
AC
2
e)
4
BR
2
=
4
AC
2
+
BC
2
(i)
{b,a}
(ii)
{b,a,c}
(iii)
{a,c,d}
(iv)
{e,c}
(v)
{b,e,d}
Question
7
7.
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
p
2
d)
a
2
+
b
2
=
c
2
e)
1
a
2
+
1
b
2
+
1
c
2
=
1
p
2
(i)
{a,b}
(ii)
{a,e,d}
(iii)
{a,b,c}
(iv)
{b,c,d}
(v)
{e,c}
Question
8
8.
In a right angled triangle △PQR, if QR = 18 cm is one of the perpendicular sides and RP = 20.59 cm is the hypotenuse, then area of the triangle =
(i)
85.00 sq.cm
(ii)
90.00 sq.cm
(iii)
87.00 sq.cm
(iv)
95.00 sq.cm
(v)
93.00 sq.cm
Question
9
9.
In a right angled triangle △PQR, if the base QR = 19 cm and the corresponding height is 10 cm, then side PQ =
(i)
13.00 cm
(ii)
7.00 cm
(iii)
15.00 cm
(iv)
5.00 cm
(v)
10.00 cm
Question
10
10.
In the given figure, △CDE is isosceles with CD = CE and DF ⟂ CE. Then
(i)
DF
2
+
EF
2
= 2
EF
.
CF
(ii)
DF
2
−
EF
2
= 2
EF
.
CF
(iii)
DF
2
−
CF
2
= 2
EF
.
CF
(iv)
DF
2
+
CF
2
= 2
EF
.
CF
Question
11
11.
In a right angled triangle △PQR, if the area is 135 sq.cm and base QR = 18 cm, then perimeter of the triangle =
(i)
53.43 cm
(ii)
56.43 cm
(iii)
59.43 cm
(iv)
51.43 cm
(v)
61.43 cm
Question
12
12.
In the given figure, △CDE is an obtuse angled triangle and CF ⟂ DE. Then
(i)
CE
2
=
CD
2
+
DE
2
+
2
DE
.
DF
(ii)
CE
2
=
CD
2
+
DE
2
+
DF
2
(iii)
CE
2
=
CD
2
+
DE
2
−
2
DE
.
DF
(iv)
CE
2
=
CD
2
+
DE
2
+
2
DF
.
EF
(v)
CE
2
=
CD
2
+
DE
2
+
2
CD
.
DE
Question
13
13.
In a right angled triangle △PQR, if the area is 144 sq.cm and base QR = 18 cm, then corresponding height of side RP =
(i)
11.96 cm
(ii)
14.96 cm
(iii)
8.96 cm
(iv)
6.96 cm
(v)
16.96 cm
Question
14
14.
In an isosceles right angled triangle △PQR, if area = 112.5 sq.cm, then corresponding height of side PQ =
(i)
20.00 cm
(ii)
10.00 cm
(iii)
12.00 cm
(iv)
18.00 cm
(v)
15.00 cm
Question
15
15.
In a right angled triangle △PQR, if the base QR = 18 cm and the corresponding height is 17 cm, then side RP =
(i)
19.76 cm
(ii)
27.76 cm
(iii)
29.76 cm
(iv)
24.76 cm
(v)
21.76 cm
Question
16
16.
In an isosceles right angled triangle △PQR, if QR = 18 cm is one of the equal sides, then corresponding height of side PQ =
(i)
18.00 cm
(ii)
23.00 cm
(iii)
13.00 cm
(iv)
21.00 cm
(v)
15.00 cm
Question
17
17.
In a right angled triangle, if the two non-hypotenuse sides are 14 cm and 48 cm, find the hypotenuse
(i)
52.00 cm
(ii)
48.00 cm
(iii)
50.00 cm
(iv)
51.00 cm
(v)
49.00 cm
Question
18
18.
In an isosceles right angled triangle △PQR, if area = 180.5 sq.cm, then side PQ =
(i)
14.00 cm
(ii)
24.00 cm
(iii)
19.00 cm
(iv)
16.00 cm
(v)
22.00 cm
Question
19
19.
In an isosceles right angled triangle △PQR, if area = 162 sq.cm, then side QR =
(i)
15.00 cm
(ii)
13.00 cm
(iii)
23.00 cm
(iv)
18.00 cm
(v)
21.00 cm
Question
20
20.
In an isosceles right angled triangle △PQR, if QR = 14 cm is one of the equal sides, then perimeter of the triangle =
(i)
44.80 cm
(ii)
52.80 cm
(iii)
47.80 cm
(iv)
42.80 cm
(v)
50.80 cm
Question
21
21.
In a right angled triangle △PQR, if the base QR = 16 cm and the corresponding height is 10 cm, then area of the triangle =
(i)
85.00 sq.cm
(ii)
75.00 sq.cm
(iii)
80.00 sq.cm
(iv)
83.00 sq.cm
(v)
77.00 sq.cm
Question
22
22.
In an isosceles right angled triangle △PQR, if RP = 15.56 cm is the hypotenuse, then corresponding height of side QR =
(i)
11.00 cm
(ii)
16.00 cm
(iii)
14.00 cm
(iv)
6.00 cm
(v)
8.00 cm
Question
23
23.
In the given figure, O is a point in the interior of the rectangle EFGH. Then
(i)
OE
2
+
OF
2
+
OG
2
+
OH
2
=
EG
2
+
FH
2
(ii)
OE
2
−
OG
2
=
OF
2
−
OH
2
(iii)
OE
2
+
OF
2
+
OG
2
+
OH
2
=
EF
2
+
FG
2
+
GH
2
+
HE
2
(iv)
OE
2
+
OG
2
=
OF
2
+
OH
2
Question
24
24.
In a right angled triangle △PQR, if QR = 17 cm is one of the perpendicular sides and RP = 23.35 cm is the hypotenuse, then side PQ =
(i)
21.00 cm
(ii)
16.00 cm
(iii)
19.00 cm
(iv)
13.00 cm
(v)
11.00 cm
Question
25
25.
In the given figure, in △DEF, 'O' is a point inside the triangle. OG ⟂ EF, OH ⟂ DF and OI ⟂ DE. Then
(i)
DI
2
+
EG
2
+
FH
2
=
OG
2
+
OH
2
+
OI
2
(ii)
DI
2
+
EG
2
+
FH
2
=
DH
2
+
FG
2
+
EI
2
(iii)
DI
2
+
EG
2
+
FH
2
=
OI
.
OG
+
OG
.
OH
+
OH
.
OI
(iv)
DI
2
+
EG
2
+
FH
2
=
OD
.
OE
+
OE
.
OF
+
OF
.
OD
Assignment Key
1) (i)
2) (ii)
3) (ii)
4) (i)
5) (iii)
6) (iii)
7) (iv)
8) (ii)
9) (v)
10) (ii)
11) (ii)
12) (i)
13) (i)
14) (v)
15) (iv)
16) (i)
17) (iii)
18) (iii)
19) (iv)
20) (iii)
21) (iii)
22) (i)
23) (iv)
24) (ii)
25) (ii)
