To solve this problem, we use the Pythagorean Theorem:
a² + b² = c²
Where
c is always the longest side (the hypotenuse), and it’s opposite the right angle.
We’ll go one triangle at a time.
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First Triangle:
Sides: 9 m and 12 m — these are the two shorter sides (legs). We need to find the hypotenuse.
So:
a = 9, b = 12
c² = 9² + 12²
c² = 81 + 144
c² = 225
c = √225 =
15 m
✔ Check: 15 is longer than both 9 and 12 → makes sense!
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Second Triangle:
One leg is 15 mm, hypotenuse is 25 mm. Find the other leg.
Let’s call the missing side “b”.
a = 15, c = 25
a² + b² = c²
15² + b² = 25²
225 + b² = 625
b² = 625 - 225 = 400
b = √400 =
20 mm
✔ Check: 20 is less than 25 → good! And 15-20-25 is a multiple of 3-4-5 → correct!
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Third Triangle:
Legs: 1.6 km and ? , hypotenuse: 2 km
Missing side = b
a = 1.6, c = 2
a² + b² = c²
(1.6)² + b² = 2²
2.56 + b² = 4
b² = 4 - 2.56 = 1.44
b = √1.44 =
1.2 km
✔ Check: 1.2 < 2 → yes, and 1.6-1.2-2 is like 4-3-5 scaled down by 0.4 → perfect!
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Fourth Triangle:
Legs: 2.7 cm and 3.6 cm → find hypotenuse.
a = 2.7, b = 3.6
c² = (2.7)² + (3.6)²
c² = 7.29 + 12.96
c² = 20.25
c = √20.25 =
4.5 cm
✔ Check: 4.5 > both 2.7 and 3.6 → yes! Also, 2.7-3.6-4.5 is 3-4-5 scaled by 0.9 → correct!
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Final Answer:
15 m, 20 mm, 1.2 km, 4.5 cm
Parent Tip: Review the logic above to help your child master the concept of pythagoras worksheet.
