Question

Question #d0959

Answer 1

`x=30`

Explanation:

`"given a fraction equal to another fraction we can solve"`
`"using the method of "color(blue)"cross-multiplication"`

`•color(white)(x)a/b=c/drArrad=bc`

`rArr25/x=x/36`

`rArrx^2=25xx36`

`color(blue)"take the square root of both sides"`

`rArrx=+-sqrt(25xx36)=sqrt25xxsqrt36=5xx6=+-30`

`color(blue)"As a check"`

Substitute this value into the equation and if both sides are equal then it is the solution.

`"left side "=cancel(25)^5/cancel(30)^6=5/6`

`"right side "=cancel(30)^5/cancel(36)^6=5/6`

`"you can check the values are also equal for "x=-30`

`rArrx=+-30" is the solution"`

Answer 2

`x=color(red)(+-30)`

Explanation:

If `25/x=x/36`
then
`x^2=25xx36` [see note below]
`color(white)(x^2)=5^2xx6^2=(5xx6)^2=30^2`
and
`x=+-30`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

In case this was not obvious, the process by which
`25/x=x/36`
was converted into
`x^2=25xx36`
involves a process often called cross multiplying
`color(white)("XXX")color(blue)(a/b=c/d)rarr color(green)(ad=bc)`

This can also be seen as follows:
Given `25/x=x/36`
If we multiply both sides by `x`, we get
`color(white)("XXX")25=(x^2)/36`
then multiplying both sides by `36` gives
`color(white)("XXX")25xx36=x^2color(white)("xxx")or x^2=25xx36`