Question

A wire of length 72cm is bent to form a right angle triangle of hypotnuse 30 cm. Find the length of other two sides.

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Answer 1

24 & 18 right

hypotenuse = 30 cm
sum of remaining two sides = 72 -30 = 42
let one is X
other 42-X

according to Pythagoras theorem
30^2 = x^2 + (42-x)^2
900= x^2+1764+x^2-84x
2x^2-84x+864=0
x^2 -42x+432 =0
solving this X = 24,18

Answer 2

24 cm and 18 cm

Step-by-step explanation:

Let their length be 'x' and 'y'.

Total length of the wire would not change.  As now, it is a triangle.

∴ total length = perimeter of Δ

                 72 = x + y + 30

            42 - x = y          ...(1)

As this is a right angled triangle:  using Pythagoras theorem,

⇒ hypotenuse² = x² + y²

⇒ 30² = x² + (42 - x)²        {from(1)}

⇒ 900 = x² + 1764 + x² - 84x

⇒ 0 = 2x² + 864 - 84x

⇒ 0 = x² - 18x - 24x + 432

⇒ 0 = (x - 18)(x - 24)

  Hence, x = 18 or 24

when x = 18, y = 24

          x = 24, y = 18