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The length of hypotenuse (in cm) of a right-angled triangle is 6 cm more than twice the length of its shortest side. If the length of its third side is 6 cm less than thrice the length of its shortest side, find the dimensions of the triangle.
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Let the shortest side be $x$ cm
Then hypotenuse = $(2x + 6)$ cm
and the third side = $(3x - 6)$ cm
$x^2 + (3x - 6)^2 = (2x + 6)^2$ (2 Marks)
$\Rightarrow 6x^2 - 60x = 0$ (1 Mark)
$\Rightarrow 6x(x - 10) = 0$ (1/2 Mark)
$\Rightarrow x = 0, x = 10$
x = 0 (rejected) (1/2 Mark)
$\therefore x = 10$
and hypotenuse = 26 cm (1/2 Mark)
and third side = 24 cm (1/2 Mark)
Then hypotenuse = $(2x + 6)$ cm
and the third side = $(3x - 6)$ cm
$x^2 + (3x - 6)^2 = (2x + 6)^2$ (2 Marks)
$\Rightarrow 6x^2 - 60x = 0$ (1 Mark)
$\Rightarrow 6x(x - 10) = 0$ (1/2 Mark)
$\Rightarrow x = 0, x = 10$
x = 0 (rejected) (1/2 Mark)
$\therefore x = 10$
and hypotenuse = 26 cm (1/2 Mark)
and third side = 24 cm (1/2 Mark)