# 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"#