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The length of the hypotenunes of …

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The length of the hypotenunes of a right tringle exceed the length of its base by 2 cm and exceed twice the length of its altitude by 1 cm find each side
  • 1 answers

Gaurav Seth 5 years ago

Let hypotenuse be a

Given, base = a-2               ---------------- (1)

Given, altitude = (a-1)/2.       ---------------- (2)


By Pythagoras theorem

a^2 = (a-2) + ((a-1)/2)^2

a^2 = (a^2-2a+1)/4 + a^2-4a+4 

4a^2 = a^2-2a+1+4(a^2-4a+4)

4a^2 = a^2-2a+1+4a^2-16a+16

a^2 - 18a + 17 =0

(a-17)(a-1) = 0

a = 17

Substitute a = 17 in (2) we get

and lenght of each side = 17 - 1/2

                                         = 16/2

                                         = 8

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