Let’s solve each triangle one by one using Pythagoras’ Theorem.
Pythagoras’ Theorem says:
In a right-angled triangle,
a² + b² = c²,
where
c is the longest side (the hypotenuse), and
a and
b are the other two sides.
We’ll use this to find each missing side.
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Triangle 1: Find ‘a’
Sides given: 6 cm and 8 cm → these are the two shorter sides.
So,
a² = 6² + 8²
a² = 36 + 64
a² = 100
a = √100 =
10 cm
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Triangle 2: Find ‘d’
Hypotenuse = 13 cm, one side = 12 cm → d is the other short side.
So,
d² + 12² = 13²
d² + 144 = 169
d² = 169 - 144 = 25
d = √25 =
5 cm
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Triangle 3: Find ‘b’
Sides given: 5 cm and 12 cm → both short sides.
b² = 5² + 12²
b² = 25 + 144
b² = 169
b = √169 =
13 cm
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Triangle 4: Find ‘e’
Hypotenuse = 5 cm, one side = 3 cm → e is the other short side.
e² + 3² = 5²
e² + 9 = 25
e² = 25 - 9 = 16
e = √16 =
4 cm
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Triangle 5: Find ‘c’
Sides given: 3 cm and 4 cm → both short sides.
c² = 3² + 4²
c² = 9 + 16
c² = 25
c = √25 =
5 cm
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Triangle 6: Find ‘f’
Hypotenuse = 10 cm, one side = 8 cm → f is the other short side.
f² + 8² = 10²
f² + 64 = 100
f² = 100 - 64 = 36
f = √36 =
6 cm
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Final Answer:
a = 10 cm
d = 5 cm
b = 13 cm
e = 4 cm
c = 5 cm
f = 6 cm
Parent Tip: Review the logic above to help your child master the concept of pythagorean theorem worksheet basic.
