Question

The hypotenuse of a right angled triangle is 6m more than twice the shortest side if the third side is 2m less than the hypotenuse find the sides of the triangle

Answer 1

Answer:

sides - 10 m, 26 m & 24 m

Hypotenuse - 26 m

Step-by-step explanation:

Let the shortest side = x m

Then hypotenuse = (2x + 6) m and third side = (2x + 4) m

By Pythagoras theorem, we have (2x + 6)² = x² + (2x + 4)²

${4x}^{2}+24x+36=x²+4x²+ \\ 16x+16$

x² - 8x - 20 = 0

(x - 10) (x + 2) = 0

x = 10 or x = -2

$but \: x \: can't \: be \: negative \: as \: side \\ of \: a \: triangle$

∴x = 10

$Hence, \: the \: sides \: of \: the \: triangle \\ are \: 10 m, \: 26m \: and \: 24m.$

$∴ \: Hypotenuse = 26m.$

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