Question

a triangle has side lengths of 3,4, and x find x if hypotenuse find x if one of the legs

Answer 1

Answer:

$Let x+2=y</p><p>$

$Also \: it \: should \: be \: noted \: that  \\ x+4=y+2x+4=y+2 is \: \\ the \: hypotenuse. \: Because \: \\ we \: know \: that \: it's \: got \: to \: \\ be \: the \: longest \: side.$

$By \: the \: Pythagoras \: theorem, \\ </p><p></p><p>(y−2) {}^{2} + y {}^{2} = (y + 2) {}^{2} \\ y {}^{2} = (y + 2) {}^{2} - (y - 2) {}^{2} \\ y {}^{2} = 4(y)(2)</p><p>$

$Since \: we \: don't \: like \: it \: when \:  y \:   \\ is \: zero, \: y=8 \\ Therefore  \: x=6. \: The \: \\ hypotenuse \: is \: 10cm \: long. \\ The \: sides \: of \: the \: triangle \: are \: \\ 6cm, 8cm \: and \: 10cm.$