The hypotenuse of a right triangle measures 29 cm. one leg is 1 cm shorter than the other. what are the lengths of the legs?

We might use Pythagorean theorem to solve this problem. We know that:

a² + b² = c²
c = 29
b = x
a = x - 1

So we can figure out that:

(x - 1)² + x² = 29²
(x - 1)² + x² = 841
x² - 1² + x² = 841
x² + 1 + x² = 841
x³ + 1 = 841              / - 1 (both sides)
x³ = 840
x = ∛840
x = 9,4353879606330667146410586879657
x ≈ 9,5

So now we just change variables into the result:

a = x - 1 = 9.5 - 1 = 8.5
b = x = 9.5
c = 29

Length of the legs is approx. 9.5 and 8.5 cm.

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