Question

What is the length of the hypotenuse of a right triangle if the two other sides are of lengths 5 and 4?

Answer 1

`approx 6.4031` units

Explanation:

Given a `triangle ABC` where `angle A` is a right angle and opposite sides are labeled `a, b and c` respectively, then Pythagoras' Theorem states that:

`a^2 = b^2+c^2`

Since the hypotenuse of a right triangle is the side opposite the right angle, in this example, the hypotenuse `=a` and either `b=5 and c=4` or vice versa. (Which makes no difference in this case]

`:. a^2 = 5^2+4^2`

`= 25 + 16 = 41`

Hence, `a = +-sqrt41 approx +-6.4031`

Since the side of a triangle must be positive,

`-> a approx 6.4031` units