Question

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?

Answer 1

`x=1" or "x=5`

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"`