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
Jun 1, 2018
Explanation:
#"since they are right angled triangles we can use"#
#color(blue)"Pythagoras' theorem"#
#"the square on the hyotenuse "="sum of squares on the"#
#color(white)(xxxxxxxxxxxxxxxxxxxxxx)"other 2 sides"#
#(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"#