In a right angled triangle, the hypotenus is (3x + 2) cm long. If the other two sides are (x + 3) cm and 3x cm how do you find x?

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In a right angled triangle, the hypotenus is (3x + 2) cm long. If the other two sides are (x + 3) cm and 3x cm how do you find x?

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Answer 1 · 2018-06-01T20:08:22

$x = 1 or x = 5$ $x=1" or "x=5$

Explanation:

$since they are right angled triangles we can use$ $"since they are right angled triangles we can use"$
$Pythagoras' theorem$ $color(blue)"Pythagoras' theorem"$

$the square on the hyotenuse = sum of squares on the$ $"the square on the hyotenuse "="sum of squares on the"$
$\times \times \times \times \times \times \times \times \times \times \times other 2 sides$ $color(white)(xxxxxxxxxxxxxxxxxxxxxx)"other 2 sides"$

${(3 x + 2)}^{2} = {(x + 3)}^{2} + {(3 x)}^{2}$ $(3x+2)^2=(x+3)^2+(3x)^2$

$cancel(9x^2)+12x+4=x^2+6x+9cancel(+9x^2)$

$"subtract "12x+4" from both sides"$

$0=x^2-6x+5$

$0=(x-1)(x-5)$

$x-1=0rArrx=1$

$x-5=0rArrx=5$

$"substitute these values into the given sides"$

$"to obtain "3,4,5 " or "8,15,17$

$"both well known "color(blue)"Pythagorean triples"$

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In a right angled triangle, the hypotenus is (3x + 2) cm long. If the other two sides are (x + 3) cm and 3x cm how do you find x?

1 Answer

Explanation:

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