Question

Use the given figure to find the length of FG

Answer 1

ANSWER


`|FG| = 19 \: units`




Step-by-step explanation


Since the altitude, |GJ| bisects the base of the triangle, it follows that, the triangle is an isosceles triangle.



This implies that,.


`|FG|=|GH|`

In terms of x, we have the equation.



`5x - 6 = 3x + 4`


We now group like terms to obtain,




`5x - 3x = 4 + 6`


This implies that,



`2x = 10`

Let us divide through by 2 to get,




`x = 5`

We can see from the diagram that,



`|FG|=5x-6`

We substitute x=5 to get,



`|FG|=5(5)-6`


This simplifies to,



`|FG|=25-6`



`|FG|=19 \: units`