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5 m.

Using Pythagoras:

Hypotenuse2 = side2 + other_side2

⇒ Hypotenuse = √(side2 + other_side2)

= √((3 m)2 + (4 m)2)

= √(9 m2 + 16 m2)

= √(25 m2)

= 5 m

3, 4, 5 is a well known Pythagorean triple - the three sides of a right angle triangle (32 + 42 = 9 + 16 = 25 = 52)

Another is: 5, 12, 13 (52 + 122 = 25 + 144 = 169 = 132)

If you multiply each of these sides by the same number (that is scale the triangle) you get other Pythagorean triples, eg

3, 4, 5 → (x2) 6, 8, 10; (x3) 9, 12, 15; (x4) 12, 16, 20; etc are all Pythagorean triples

5, 12, 13 → (x2) 10, 24, 26; (x3) 15, 26, 39; (x4) 20, 48, 52; etc are also all Pythagorean triples.

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Q: What is the length of the hypotenuse of a right angled triangle where one side equals 4m and the other equals 3m?
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