Question

The lengths of two sides of a right angled triangle are 20 cm and 30 cm.

Calculate the length of the third side, if it is:
(a) the hypotenuse
(b) not the hypotenuse

Answer 1

Answers:

• Part (a) 10*sqrt(13)
• Part (b) 10*sqrt(5)

Those values are exact. They approximate to:

10*sqrt(13) = 36.0555

10*sqrt(5) = 22.3607

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Step-by-step explanation:

Part (a)

If the unknown third side is the hypotenuse then we need to find the value of c when a = 20 and b = 30.

Apply the pythagorean theorem

a^2 + b^2 = c^2

20^2 + 30^2 = c^2

400 + 900 = c^2

1300 = c^2

c^2 = 1300

c = sqrt(1300)

c = sqrt(100*13)

c = sqrt(100)*sqrt(13)

c = 10*sqrt(13) .... exact length

c = 36.0555 ...... approximate length

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Part (b)

If the third side is not the hypotenuse then that must mean c = 30 is the hypotenuse as this side is larger than the 20 cm side. The hypotenuse is always the longest side.

Let a = 20 be the known leg. Let's find the other unknown leg b using the pythagorean theorem.

a^2 + b^2 = c^2

20^2 + b^2 = 30^2

400 + b^2 = 900

b^2 = 900-400

b^2 = 500

b = sqrt(500)

b = sqrt(100*5)

b = sqrt(100)*sqrt(5)

b = 10*sqrt(5) ..... exact length

b = 22.3607 ....... approximate length