Question

Use the given figure to find the length of FG

Answer 1

ANSWER

$|FG| = 19 \: units$




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,


$|FG|=25-6$


$|FG|=19 \: units$