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 90 sq.cm and corresponding height of side QR = 18 cm, then perimeter of the triangle =
(i)
48.59 cm
(ii)
45.59 cm
(iii)
43.59 cm
(iv)
51.59 cm
(v)
53.59 cm
Question
2
2.
A vehicle goes 11 km West and then 10 km South. How far is it from its starting point ?
(i)
13.87 km
(ii)
14.87 km
(iii)
12.87 km
(iv)
16.87 km
(v)
15.87 km
Question
3
3.
In an isosceles right angled triangle △PQR, if corresponding height to the base QR is 19 cm, then corresponding height of side PQ =
(i)
24.00 cm
(ii)
16.00 cm
(iii)
19.00 cm
(iv)
22.00 cm
(v)
14.00 cm
Question
4
4.
In an equilateral triangle ABC, the side BC is trisected at D. Then
(i)
3 AD
2
=
7 AB
2
(ii)
7 AD
2
=
9 AB
2
(iii)
7 AD
2
=
3 AB
2
(iv)
9 AD
2
=
7 AB
2
Question
5
5.
In a right angled triangle △PQR, if the area is 135 sq.cm and base QR = 15 cm, then perimeter of the triangle =
(i)
56.43 cm
(ii)
53.43 cm
(iii)
51.43 cm
(iv)
59.43 cm
(v)
61.43 cm
Question
6
6.
In an isosceles right angled triangle △PQR, if QR = 11 cm is one of the equal sides, then corresponding height of side RP =
(i)
5.78 cm
(ii)
8.78 cm
(iii)
9.78 cm
(iv)
6.78 cm
(v)
7.78 cm
Question
7
7.
In the given figure, △BCD is an obtuse angled triangle and BE ⟂ CD. Then
(i)
BD
2
=
BC
2
+
CD
2
+
2
BC
.
CD
(ii)
BD
2
=
BC
2
+
CD
2
+
CE
2
(iii)
BD
2
=
BC
2
+
CD
2
−
2
CD
.
CE
(iv)
BD
2
=
BC
2
+
CD
2
+
2
CE
.
DE
(v)
BD
2
=
BC
2
+
CD
2
+
2
CD
.
CE
Question
8
8.
In the given figure, FGH is a triangle and 'O' is a point inside △FGH. The angular bisector of ∠GOF, ∠HOG & ∠FOH meet FG, GH & HF at I, J & K respectively . Then
(i)
FI . GJ . HK = OF . OG . OH
(ii)
FI . GJ . HK = IG . JH . KF
(iii)
FI . GJ . HK = OI . OJ . OK
(iv)
FI . GJ . HK = FG . GH . HF
(v)
FI . GJ . HK = IJ . JK . KI
Question
9
9.
In a right angled triangle △PQR, if QR = 12 cm, PQ = 18 cm are the lengths of perpendicular sides , then side RP =
(i)
18.63 cm
(ii)
21.63 cm
(iii)
16.63 cm
(iv)
24.63 cm
(v)
26.63 cm
Question
10
10.
In an isosceles right angled triangle △PQR, if area = 72 sq.cm, then corresponding height of side PQ =
(i)
15.00 cm
(ii)
7.00 cm
(iii)
9.00 cm
(iv)
17.00 cm
(v)
12.00 cm
Question
11
11.
In an isosceles right angled triangle △PQR, if QR = 19 cm is one of the equal sides, then corresponding height of side PQ =
(i)
24.00 cm
(ii)
19.00 cm
(iii)
22.00 cm
(iv)
16.00 cm
(v)
14.00 cm
Question
12
12.
In a right angled triangle △PQR, if QR = 17 cm, PQ = 18 cm are the lengths of perpendicular sides , then corresponding height of side RP =
(i)
17.36 cm
(ii)
7.36 cm
(iii)
9.36 cm
(iv)
12.36 cm
(v)
15.36 cm
Question
13
13.
In a right angled triangle △PQR, if the area is 70 sq.cm and corresponding height of side QR = 10 cm, then corresponding height of side RP =
(i)
8.14 cm
(ii)
10.14 cm
(iii)
7.14 cm
(iv)
6.14 cm
(v)
9.14 cm
Question
14
14.
The foot of a ladder resting on a wall from the foot of the wall is 14 m. If the height of the top of the ladder from ground is 12 m, find the length of the ladder
(i)
19.44 m
(ii)
18.44 m
(iii)
20.44 m
(iv)
16.44 m
(v)
17.44 m
Question
15
15.
In a right angled triangle △PQR, if QR = 15 cm is one of the perpendicular sides and RP = 23.43 cm is the hypotenuse, then side PQ =
(i)
23.00 cm
(ii)
18.00 cm
(iii)
13.00 cm
(iv)
21.00 cm
(v)
15.00 cm
Question
16
16.
In a right angled triangle △PQR, if the base QR = 14 cm and the corresponding height is 12 cm, then side RP =
(i)
23.44 cm
(ii)
15.44 cm
(iii)
21.44 cm
(iv)
18.44 cm
(v)
13.44 cm
Question
17
17.
In the given figure, △FGH, FI ⟂ GH. Which of the following are true?
a)
FI
2
=
2
GI
.
HI
b)
FG
2
−
FH
2
=
GI
2
−
HI
2
c)
FG
2
−
GI
2
=
FH
2
−
HI
2
d)
FG
2
+
GI
2
=
FH
2
+
HI
2
e)
FG
2
+
FH
2
=
GI
2
+
HI
2
(i)
{e,a,b}
(ii)
{d,c}
(iii)
{d,c,b}
(iv)
{b,c}
(v)
{a,b}
Question
18
18.
In an isosceles right angled triangle △PQR, if perimeter = 54.63 cm, then side QR =
(i)
21.00 cm
(ii)
16.00 cm
(iii)
19.00 cm
(iv)
11.00 cm
(v)
13.00 cm
Question
19
19.
In the given figure, △ABC is isosceles with AB = AC and BD ⟂ AC. Then
(i)
BD
2
+
AD
2
= 2
CD
.
AD
(ii)
BD
2
−
AD
2
= 2
CD
.
AD
(iii)
BD
2
+
CD
2
= 2
CD
.
AD
(iv)
BD
2
−
CD
2
= 2
CD
.
AD
Question
20
20.
In an isosceles right angled triangle △PQR, if RP = 14.14 cm is the hypotenuse, then corresponding height of side RP =
(i)
6.07 cm
(ii)
5.07 cm
(iii)
9.07 cm
(iv)
7.07 cm
(v)
8.07 cm
Question
21
21.
In an isosceles right angled triangle △PQR, if area = 60.5 sq.cm, then corresponding height of side QR =
(i)
8.00 cm
(ii)
16.00 cm
(iii)
11.00 cm
(iv)
14.00 cm
(v)
6.00 cm
Question
22
22.
In a right angled triangle △PQR, if QR = 13 cm is one of the perpendicular sides and RP = 17.03 cm is the hypotenuse, then corresponding height of side PQ =
(i)
8.00 cm
(ii)
13.00 cm
(iii)
18.00 cm
(iv)
10.00 cm
(v)
16.00 cm
Question
23
23.
In an isosceles right angled triangle △PQR, if RP = 24.04 cm is the hypotenuse, then side QR =
(i)
14.00 cm
(ii)
20.00 cm
(iii)
12.00 cm
(iv)
17.00 cm
(v)
22.00 cm
Question
24
24.
In an isosceles right angled triangle △PQR, if RP = 19.8 cm is the hypotenuse, then area of the triangle =
(i)
93.00 sq.cm
(ii)
95.00 sq.cm
(iii)
98.00 sq.cm
(iv)
101.00 sq.cm
(v)
103.00 sq.cm
Question
25
25.
In the given figure, in △EFG, 'O' is a point inside the triangle. OH ⟂ FG, OI ⟂ EG and OJ ⟂ EF. Then
(i)
EJ
2
+
FH
2
+
GI
2
=
OH
2
+
OI
2
+
OJ
2
(ii)
EJ
2
+
FH
2
+
GI
2
=
EI
2
+
GH
2
+
FJ
2
(iii)
EJ
2
+
FH
2
+
GI
2
=
OE
.
OF
+
OF
.
OG
+
OG
.
OE
(iv)
EJ
2
+
FH
2
+
GI
2
=
OJ
.
OH
+
OH
.
OI
+
OI
.
OJ
Assignment Key
1) (i)
2) (ii)
3) (iii)
4) (iv)
5) (i)
6) (v)
7) (v)
8) (ii)
9) (ii)
10) (v)
11) (ii)
12) (iv)
13) (i)
14) (ii)
15) (ii)
16) (iv)
17) (iv)
18) (ii)
19) (iv)
20) (iv)
21) (iii)
22) (ii)
23) (iv)
24) (iii)
25) (ii)
