Pythagoras: finding a shorter side

The Maths Habit

1

Find the length of the hypotenuse, c.

45 cm24 cmc
51 cm2

Find the length of the hypotenuse, c.

44 mm33 mmc
55 mm3

Find the length of the hypotenuse, c.

84 cm13 cmc
85 cm

The rope stays the same length. Peg it further from the pole. Does it reach higher or lower up the pole?

pegged nearpegged further out

Lower. More of the rope goes along the ground, so less goes up.

What is the value of a?

a + 4 = 10a = 6
a + 9 = 25a = 16
a2 + 9 = 25a = 4

bac
a2 + b2 = c2
c is the hypotenuse.
  1. A short side:
    x2 = c2 − b2
  2. 1Square the two sides you know.
  3. 2Subtract.
  4. 3Square root.

Find the length of the side marked x.

x16 cm34 cm
1Square the two sides you know.
x2=342−162
x2=1156−256
2Subtract.
x2=900
3Square root.
x=√900=30cm

Find the length of the side marked x.

x40 cm58 cm
1Square the two sides you know.
x2=582−402
x2=3364−1600
2Subtract.
x2=1764
3Square root.
x=√1764=42cm

Find the length of the side marked x.

x16 cm34 cm
1Square the two sides you know.
x2=342−162
x2=1156−256
2Subtract.
x2=900
3Square root.
x=√900=30cm
1Square the two sides you know.2Subtract.3Square root.

Find the length of the side marked x.

20 cmx52 cm
1Square the two sides you know.
x2=522−202
x2=2704−400
2Subtract.
x2=2304
3Square root.
x=√2304=48cm

Find the length of the side marked x.

x16 cm34 cm
1Square the two sides you know.
x2=342−162
x2=1156−256
2Subtract.
x2=900
3Square root.
x=√900=30cm
1Square the two sides you know.2Subtract.3Square root.

Find the length of the side marked x.

x27 m45 m
1Square the two sides you know.
x2=452−272
x2=2025−729
2Subtract.
x2=1296
3Square root.
x=√1296=36m

Find the length of the side marked x.

x16 cm34 cm
1Square the two sides you know.
x2=342−162
x2=1156−256
2Subtract.
x2=900
3Square root.
x=√900=30cm
1Square the two sides you know.2Subtract.3Square root.

Find the length of the side marked x.

25 cmx65 cm
1Square the two sides you know.
x2=652−252
x2=4225−625
2Subtract.
x2=3600
3Square root.
x=√3600=60cm

Find the length of the side marked x.

x33 cm65 cm
1Square the two sides you know.
x2=652−332
x2=4225−1089
2Subtract.
x2=3136
3Square root.
x=√3136=56cm

Find the height of the rectangle, x.

28 cmx35 cm
1Square the two sides you know.
x2=352−282
x2=1225−784
2Subtract.
x2=441
3Square root.
x=√441=21cm

Find the length of the side marked x.

x33 cm65 cm
1Square the two sides you know.
x2=652−332
x2=4225−1089
2Subtract.
x2=3136
3Square root.
x=√3136=56cm
1Square the two sides you know.2Subtract.3Square root.

Find the length of the side marked x.

45 cmx53 cm
1Square the two sides you know.
x2=532−452
x2=2809−2025
2Subtract.
x2=784
3Square root.
x=√784=28cm

Find the length of the side marked x.

x33 cm65 cm
1Square the two sides you know.
x2=652−332
x2=4225−1089
2Subtract.
x2=3136
3Square root.
x=√3136=56cm
1Square the two sides you know.2Subtract.3Square root.

Find the height of the rectangle, x.

60 mx75 m
1Square the two sides you know.
x2=752−602
x2=5625−3600
2Subtract.
x2=2025
3Square root.
x=√2025=45m

Find the length of the side marked x.

x33 cm65 cm
1Square the two sides you know.
x2=652−332
x2=4225−1089
2Subtract.
x2=3136
3Square root.
x=√3136=56cm
1Square the two sides you know.2Subtract.3Square root.

Find the length of the side marked x.

x48 cm73 cm
1Square the two sides you know.
x2=732−482
x2=5329−2304
2Subtract.
x2=3025
3Square root.
x=√3025=55cm

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

  1. Hypotenuse 50 cm, short side 14 cm.
    Other short side 48 cm.

    Right

  2. Hypotenuse 26 cm, short side 10 cm.
    x2 = 262 + 102.

    Wrong: subtract

  3. Hypotenuse 17 m, short side 15 m.
    Other short side 8 m.

    Right

  4. Hypotenuse 41 cm, short side 40 cm.
    Other short side 81 cm.

    Wrong: 9 cm

Pythagoras: finding a shorter side worksheet, page 1

Pythagoras: finding a shorter side worksheet, page 2

Answer sheet

  1. Hypotenuse 9 cm, short side 5 cm. Find the other short side to 1 decimal place.

    7.5 cm

  2. A rectangle is 12 cm wide. Its diagonal is 13 cm. Find its area.

    60 cm²

  3. A triangle has sides 13 cm, 13 cm and 10 cm. Find its height.

    12 cm

  1. Find the length x.

    80 cm
    x60 cm100 cm1Square the twosides you know.x2=1002−602x2=−2Subtract.x2=3Square root.x=√=cm

  2. Find the length x.

    39 cm
    80 cmx89 cm1Square the twosides you know.x2=2−2x2=−2Subtract.x2=3Square root.x=√=cm

  3. A triangle has a right angle. Its hypotenuse is 61 m and one short side is 60 m. Find the other short side.

    11 m
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