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, if one of the angles is 33.69°, find the third angle
(i)
56.31°
(ii)
86.31°
(iii)
61.31°
(iv)
66.31°
(v)
71.31°
Question
2
2.
In a right angled triangle, if the two non-hypotenuse sides are 10 cm and 24 cm, find the hypotenuse
(i)
24.00 cm
(ii)
25.00 cm
(iii)
27.00 cm
(iv)
26.00 cm
(v)
28.00 cm
Question
3
3.
In the given figure, O is a point in the interior of the rectangle DEFG. Then
(i)
OD
2
+
OE
2
+
OF
2
+
OG
2
=
DE
2
+
EF
2
+
FG
2
+
GD
2
(ii)
OD
2
+
OF
2
=
OE
2
+
OG
2
(iii)
OD
2
+
OE
2
+
OF
2
+
OG
2
=
DF
2
+
EG
2
(iv)
OD
2
−
OF
2
=
OE
2
−
OG
2
Question
4
4.
In a right angled triangle △PQR, if QR = 13 cm, PQ = 20 cm are the lengths of perpendicular sides , then perimeter of the triangle =
(i)
53.85 cm
(ii)
51.85 cm
(iii)
61.85 cm
(iv)
56.85 cm
(v)
59.85 cm
Question
5
5.
In a right angled triangle △PQR, if the area is 95 sq.cm and base QR = 19 cm, then corresponding height of side QR =
(i)
10.00 cm
(ii)
13.00 cm
(iii)
7.00 cm
(iv)
5.00 cm
(v)
15.00 cm
Question
6
6.
In a right angled triangle △PQR, if QR = 19 cm, PQ = 12 cm are the lengths of perpendicular sides , then corresponding height of side RP =
(i)
15.15 cm
(ii)
7.15 cm
(iii)
5.15 cm
(iv)
13.15 cm
(v)
10.15 cm
Question
7
7.
In the given figure, DEFG is a rhombus. Which of the following are true?
a)
DE
2
+
EF
2
+
FG
2
+
DG
2
=
DF
2
+
EG
2
b)
EF
2
+
FG
2
=
EG
2
c)
2
DE
2
=
DF
2
+
EG
2
d)
DE
2
+
EF
2
=
DF
2
e)
4
DE
2
=
DF
2
+
EG
2
(i)
{a,e}
(ii)
{b,a}
(iii)
{d,b,a}
(iv)
{c,e}
(v)
{c,e,a}
Question
8
8.
Two poles of heights 6 m and 13 m stand vertically on a plane ground. If the distance between their feet is 14 m, find the distance between their tops
(i)
14.65 m
(ii)
15.65 m
(iii)
13.65 m
(iv)
16.65 m
(v)
17.65 m
Question
9
9.
In an isosceles right angled triangle △PQR, if RP = 14.14 cm is the hypotenuse, then side QR =
(i)
15.00 cm
(ii)
10.00 cm
(iii)
13.00 cm
(iv)
5.00 cm
(v)
7.00 cm
Question
10
10.
In an isosceles right angled triangle △PQR, if area = 112.5 sq.cm, then corresponding height of side PQ =
(i)
18.00 cm
(ii)
12.00 cm
(iii)
10.00 cm
(iv)
20.00 cm
(v)
15.00 cm
Question
11
11.
In a right angled triangle △PQR, if QR = 19 cm, PQ = 12 cm are the lengths of perpendicular sides , then area of the triangle =
(i)
102.00 sq.cm
(ii)
114.00 sq.cm
(iii)
120.00 sq.cm
(iv)
129.00 sq.cm
Question
12
12.
In an isosceles right angled triangle △PQR, if RP = 16.97 cm is the hypotenuse, then corresponding height of side RP =
(i)
7.49 cm
(ii)
8.49 cm
(iii)
9.49 cm
(iv)
6.49 cm
(v)
10.49 cm
Question
13
13.
In the given figure, △CED is right-angled at E, EF ⟂ CD.
CD
= c,
ED
= a,
CE
= b and
EF
= p.
Which of the following are true?
a)
ab
=
pc
b)
1
a
2
+
1
b
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)
1
a
2
+
1
b
2
=
1
c
2
+
1
p
2
(i)
{d,a}
(ii)
{d,e,c}
(iii)
{e,b}
(iv)
{d,a,b}
(v)
{a,b,c}
Question
14
14.
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
=
OD
.
OE
+
OE
.
OF
+
OF
.
OD
(ii)
DI
2
+
EG
2
+
FH
2
=
OI
.
OG
+
OG
.
OH
+
OH
.
OI
(iii)
DI
2
+
EG
2
+
FH
2
=
OG
2
+
OH
2
+
OI
2
(iv)
DI
2
+
EG
2
+
FH
2
=
DH
2
+
FG
2
+
EI
2
Question
15
15.
In an isosceles right angled triangle △PQR, if area = 144.5 sq.cm, then corresponding height of side RP =
(i)
15.02 cm
(ii)
7.02 cm
(iii)
17.02 cm
(iv)
12.02 cm
(v)
9.02 cm
Question
16
16.
In the given figure, △EFG is a triangle with EH being the median of FG. Then
(i)
EF
2
+
EG
2
=
2
FH
2
+
2
EH
2
(ii)
EF
2
+
EG
2
=
EH
2
(iii)
EF
2
+
EG
2
=
FG
2
(iv)
EF
2
+
EG
2
=
2
HG
2
+
2
EH
2
(v)
EF
2
+
EG
2
=
2
FH
2
+
2
HG
2
Question
17
17.
In an isosceles right angled triangle △PQR, if area = 128 sq.cm, then corresponding height of side QR =
(i)
11.00 cm
(ii)
19.00 cm
(iii)
21.00 cm
(iv)
16.00 cm
(v)
13.00 cm
Question
18
18.
In the given figure, △CDE is an obtuse angled triangle and CF ⟂ DE. Then
(i)
CE
2
=
CD
2
+
DE
2
+
2
DF
.
EF
(ii)
CE
2
=
CD
2
+
DE
2
+
2
DE
.
DF
(iii)
CE
2
=
CD
2
+
DE
2
+
2
CD
.
DE
(iv)
CE
2
=
CD
2
+
DE
2
−
2
DE
.
DF
(v)
CE
2
=
CD
2
+
DE
2
+
DF
2
Question
19
19.
In an isosceles right angled triangle △PQR, if corresponding height to the base QR is 10 cm, then corresponding height of side QR =
(i)
13.00 cm
(ii)
5.00 cm
(iii)
15.00 cm
(iv)
7.00 cm
(v)
10.00 cm
Question
20
20.
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
−
CF
2
= 2
EF
.
CF
(iii)
DF
2
+
CF
2
= 2
EF
.
CF
(iv)
DF
2
+
EF
2
= 2
EF
.
CF
Question
21
21.
In a right angled triangle △PQR, if QR = 20 cm, PQ = 17 cm are the lengths of perpendicular sides , then corresponding height of side QR =
(i)
17.00 cm
(ii)
14.00 cm
(iii)
22.00 cm
(iv)
20.00 cm
(v)
12.00 cm
Question
22
22.
In an isosceles right angled triangle △PQR, if QR = 10 cm is one of the equal sides, then side RP =
(i)
17.14 cm
(ii)
9.14 cm
(iii)
19.14 cm
(iv)
14.14 cm
(v)
11.14 cm
Question
23
23.
In an isosceles right angled triangle △PQR, if QR = 15 cm is one of the equal sides, then area of the triangle =
(i)
139.50 sq.cm
(ii)
112.50 sq.cm
(iii)
130.50 sq.cm
(iv)
87.50 sq.cm
(v)
104.50 sq.cm
Question
24
24.
In an isosceles right angled triangle △PQR, if corresponding height to the base QR is 14 cm, then area of the triangle =
(i)
95.00 sq.cm
(ii)
103.00 sq.cm
(iii)
101.00 sq.cm
(iv)
98.00 sq.cm
(v)
93.00 sq.cm
Question
25
25.
In a right angled triangle △PQR, if the area is 90 sq.cm and base QR = 18 cm, then perimeter of the triangle =
(i)
53.59 cm
(ii)
43.59 cm
(iii)
51.59 cm
(iv)
45.59 cm
(v)
48.59 cm
Assignment Key
1) (i)
2) (iv)
3) (ii)
4) (iv)
5) (i)
6) (v)
7) (i)
8) (ii)
9) (ii)
10) (v)
11) (ii)
12) (ii)
13) (v)
14) (iv)
15) (iv)
16) (i)
17) (iv)
18) (ii)
19) (v)
20) (i)
21) (i)
22) (iv)
23) (ii)
24) (iv)
25) (v)
