Pythagoras’ Theorem (Copy)
1.
A right triangle has legs 6 cm and 8 cm.
Find the hypotenuse.
2.
A right triangle has hypotenuse 13 cm and one leg 12 cm.
Find the other leg.
3.
The sides of a right triangle are in the ratio 5:12:13.
If the hypotenuse is 26 cm, find the other two sides.
4.
A ladder leans against a wall, reaching 12 m high. The foot of the ladder is 5 m from the wall.
Find the length of the ladder.
5.
A rectangle has diagonal 25 cm and side 20 cm.
Find the other side.
6.
A triangle has sides 7 cm and 24 cm, hypotenuse 25 cm.
Verify that it is a right triangle.
7.
A right triangle has base 9 cm and hypotenuse 15 cm.
Find the perpendicular.
8.
A square has diagonal 10 cm.
Find its side length.
9.
The diagonal of a rectangle is 17 cm, one side 8 cm.
Find the other side.
10.
A rectangular field is 80 m by 150 m.
Find the length of its diagonal.
11.
A triangle has sides 10 cm, 24 cm, and 26 cm.
Show that it is a right triangle.
12.
A ladder 20 m long rests against a wall. The foot is 12 m from the wall.
Find how high the ladder reaches.
13.
The sides of a right triangle are 15 cm and 20 cm.
Find the hypotenuse.
14.
A TV screen is 80 cm wide and 60 cm tall.
Find its diagonal length.
15.
A rhombus has diagonals 16 cm and 30 cm.
Find its side length.
16.
A triangle has sides 8 cm, 15 cm, and 17 cm.
Check if it is right-angled.
17.
A rectangle has perimeter 50 cm. One side is 12 cm.
Find its diagonal.
18.
A kite has diagonals 12 cm and 16 cm.
Find the length of each side.
19.
A right triangle has legs 9 m and 40 m.
Find the hypotenuse.
20.
A square has area 98 m².
Find the length of its diagonal.
21.
A triangle has hypotenuse 29 cm and one side 20 cm.
Find the other side.
22.
A ladder 13 m long leans against a wall. If it reaches 12 m high, find how far the foot is from the wall.
23.
The diagonal of a rectangle is 25 cm and one side 7 cm.
Find the other side.
24.
A right triangle has hypotenuse 34 cm and one side 30 cm.
Find the other side.
25.
A triangle has sides 9 cm, 40 cm, and 41 cm.
Verify it is right-angled.
26.
A cuboid has edges 6 cm, 8 cm, and 24 cm.
Find the length of its space diagonal.
27.
A cube has side 5 cm.
Find the length of its space diagonal.
28.
A triangle has hypotenuse 10 cm and one side 8 cm.
Find the other side.
29.
The diagonal of a square is 14 cm.
Find its area.
30.
A triangle has base 15 cm and height 20 cm.
Find the hypotenuse.
1.
Hypotenuse = √(6²+8²) = √(36+64) = √100 = 10 cm.
2.
Other leg = √(13²−12²) = √(169−144) = √25 = 5 cm.
3.
Scale factor = 26 ÷ 13 = 2.
Sides = 5×2=10 cm, 12×2=24 cm.
So sides = 10 cm and 24 cm.
4.
Ladder = √(12²+5²) = √(144+25) = √169 = 13 m.
5.
Other side = √(25²−20²) = √(625−400) = √225 = 15 cm.
6.
Check: 7²+24² = 49+576=625.
25²=625 → equal.
So yes, it is a right triangle.
7.
Perpendicular = √(15²−9²) = √(225−81) = √144 = 12 cm.
8.
Side = diagonal ÷ √2 = 10 ÷ √2 = 5√2 ≈ 7.07 cm.
9.
Other side = √(17²−8²) = √(289−64) = √225 = 15 cm.
10.
Diagonal = √(80²+150²) = √(6400+22500) = √28900 = 170 m.
11.
Check: 10²+24² = 100+576=676.
26²=676 → equal.
So yes, it is a right triangle.
12.
Height = √(20²−12²) = √(400−144) = √256 = 16 m.
13.
Hypotenuse = √(15²+20²) = √(225+400) = √625 = 25 cm.
14.
Diagonal = √(80²+60²) = √(6400+3600) = √10000 = 100 cm.
15.
Half diagonals = 8 and 15.
Side = √(8²+15²) = √(64+225)=√289= 17 cm.
16.
Check: 8²+15²=64+225=289.
17²=289.
So yes, right-angled.
17.
Perimeter=50, so l+w=25. One side=12 → other=13.
Diagonal=√(12²+13²)=√(144+169)=√313≈ 17.7 cm.
18.
Half diagonals = 6 and 8.
Side = √(6²+8²) = √(36+64) = √100 = 10 cm.
So each side=10 cm.
19.
Hypotenuse = √(9²+40²) = √(81+1600)=√1681= 41 m.
20.
Side=√98 ≈ 9.90 m.
Diagonal=side√2=√(98×2)=√196=14.
So diagonal=14 m.
21.
Other side = √(29²−20²) = √(841−400) = √441= 21 cm.
22.
Foot distance=√(13²−12²)=√(169−144)=√25= 5 m.
23.
Other side=√(25²−7²)=√(625−49)=√576= 24 cm.
24.
Other side=√(34²−30²)=√(1156−900)=√256= 16 cm.
25.
Check: 9²+40²=81+1600=1681.
41²=1681.
So yes, right-angled.
26.
Space diagonal=√(6²+8²+24²)=√(36+64+576)=√676= 26 cm.
27.
Space diagonal=side√3=5√3≈ 8.66 cm.
28.
Other side=√(10²−8²)=√(100−64)=√36= 6 cm.
29.
Side=14/√2=7√2.
Area=side²=(7√2)²=98.
So 98 cm².
30.
Hypotenuse=√(15²+20²)=√(225+400)=√625= 25 cm.