Pythagoras: finding the hypotenuse

The Maths Habit

You walk to the gate. Round the edge, or straight across: which way is shorter?

Straight across. It is the longest side of the triangle, but shorter than the other two put together.

Work out.

7²49

10²100

√497

Right angle: A quarter turn. It is marked with a small square.

Hypotenuse: The longest side of a triangle with a right angle. It is opposite the right angle.

Square: A number times itself.

Square root: Undoes squaring: the number that was squared.

a² + b² = c²

c is the hypotenuse.

1Square the two short sides.
c²=3²+4²=9+16
2Add.
c²=25
3Square root.
c=√25=5cm

Find the length of the hypotenuse, c.

1Square the two short sides.

c²=24²+32²

c²=576+1024

2Add.

c²=1600

3Square root.

c=√1600=40cm

Find the length of the hypotenuse, c.

1Square the two short sides.

c²=20²+48²

c²=400+2304

2Add.

c²=2704

3Square root.

c=√2704=52cm

Find the length of the hypotenuse, c.

1Square the two short sides.

c²=24²+32²

c²=576+1024

2Add.

c²=1600

3Square root.

c=√1600=40cm

1Square the two short sides.2Add.3Square root.

Find the length of the hypotenuse, c.

1Square the two short sides.

c²=27²+36²

c²=729+1296

2Add.

c²=2025

3Square root.

c=√2025=45cm

Find the length of the hypotenuse, c.

1Square the two short sides.

c²=24²+32²

c²=576+1024

2Add.

c²=1600

3Square root.

c=√1600=40cm

1Square the two short sides.2Add.3Square root.

Find the length of the hypotenuse, c.

1Square the two short sides.

c²=24²+70²

c²=576+4900

2Add.

c²=5476

3Square root.

c=√5476=74m

Find the length of the hypotenuse, c.

1Square the two short sides.

c²=24²+32²

c²=576+1024

2Add.

c²=1600

3Square root.

c=√1600=40cm

1Square the two short sides.2Add.3Square root.

Find the length of the hypotenuse, c.

1Square the two short sides.

c²=28²+45²

c²=784+2025

2Add.

c²=2809

3Square root.

c=√2809=53cm

Which side is the hypotenuse?

1

B

2

C

3

A

Find the length of the hypotenuse, c.

1Square the two short sides.

c²=36²+48²

c²=1296+2304

2Add.

c²=3600

3Square root.

c=√3600=60cm

Find the length of the diagonal, c.

1Square the two short sides.

c²=25²+60²

c²=625+3600

2Add.

c²=4225

3Square root.

c=√4225=65cm

Find the length of the hypotenuse, c.

1Square the two short sides.

c²=36²+48²

c²=1296+2304

2Add.

c²=3600

3Square root.

c=√3600=60cm

1Square the two short sides.2Add.3Square root.

Find the length of the hypotenuse, c.

1Square the two short sides.

c²=48²+64²

c²=2304+4096

2Add.

c²=6400

3Square root.

c=√6400=80cm

Find the length of the hypotenuse, c.

1Square the two short sides.

c²=36²+48²

c²=1296+2304

2Add.

c²=3600

3Square root.

c=√3600=60cm

1Square the two short sides.2Add.3Square root.

Find the length of the diagonal, c.

1Square the two short sides.

c²=32²+60²

c²=1024+3600

2Add.

c²=4624

3Square root.

c=√4624=68m

Find the length of the hypotenuse, c.

1Square the two short sides.

c²=36²+48²

c²=1296+2304

2Add.

c²=3600

3Square root.

c=√3600=60cm

1Square the two short sides.2Add.3Square root.

Find the length of the hypotenuse, c.

1Square the two short sides.

c²=48²+55²

c²=2304+3025

2Add.

c²=5329

3Square root.

c=√5329=73cm

Is it right?
Thumbs up: right. Thumbs down: wrong.

Short sides 60 cm and 80 cm. c = 100 cm.
Right
Short sides 50 cm and 120 cm. c = 170 cm.
Wrong: 130 cm
c² = 289, so c = 289.
Wrong: 17
Short sides 80 m and 150 m. c = 170 m.
Right

Pythagoras: finding the hypotenuse worksheet, page 1

Pythagoras: finding the hypotenuse worksheet, page 2

Answer sheet

Short sides 4 cm and 7 cm. Find c to 1 decimal place.
8.1 cm
The hypotenuse is 13 cm and one short side is 5 cm. Find the other short side.
12 cm
A triangle has sides 7 cm, 9 cm and 12 cm. Does it have a right angle?
No: 130, not 144

Find the length c.
75 cm
Find the length c.
89 cm
A triangle has a right angle. Its short sides are 35 m and 84 m. Find the length of its hypotenuse.
91 m

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