Question

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Answer 1

Answer: 17 cm, 15 cm, 8 cm.

Step by step explanation:

Let hypotenuse of right angled triangle be x.

Now, Given that:

Base = x - 2

Altitude = (x - 1)/2

By Pythagoras theorem,

(Hyp.)² = (Base)² + (altitude)²

x² = (x - 2)² + [(x - 1)/2)]²

x² = x² - 4x + 4 + (x² - 2x + 1)/4

4x² = 4(x² - 4x + 4) + x² - 2x + 1

4x² = 4x² - 16x + 16 + x² - 2x + 1

0 = x² - 18a + 17

x² - 17a + a + 17 = 0

(x - 17)(x - 1) = 0

x = 17 cm

Finding lengths of each side,

Base = x - 2 = 17 - 2 = 15 cm

Altitude = (x - 1) / 2 = (17 - 1)/2 = 8 cm

Thus, the lengths of the traingle are 17 cm, 15 cm, 8 cm.

Answer 2

Let hypotenuse be a

Given, base = a-2

Given, altitude = (a-1)/2

By Pythagoras theorem

a² = (a-2) + {(a-1)/2}²

a² = ( a²-2a +1) /4+ a²-4a + 4

4a² = a²-2a+1+4(a²-4a + 4)

4a² = a²-2a+1+4a²-16a+16

a²-18a+17 = 0

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

a = 17

Substitute a = 17 in 2 we get

and length of each side = 17 - 1/2

= 16/2

= 8

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