Answer:
The height of triangle EFG is 9 units
Step-by-step explanation:
see the attached figure to better understand the problem
step 1
Find the area of a square ABCD
The area of a square is equal to
[tex]A=b^2[/tex]
where
b is the length side of the square
we have
[tex]b=AB=6\ units[/tex]
substitute
[tex]A=6^2=36\ units^2[/tex]
step 2
Find the height of triangle EFG
The area of triangle EFG is equal to
[tex]A=\frac{1}{2}(b)(h)[/tex]
where
b is the base of triangle
h is the height of triangle
we have
[tex]b=EG=8\ units[/tex]
[tex]A=36\ units^2[/tex] ---> area of triangle EFG is the same that the area of square ABCD
substitute the given values in the formula
[tex]36=\frac{1}{2}(8)(h)[/tex]
solve for h
[tex]36=4h\\h=9\ units[/tex]
therefore
The height of triangle EFG is 9 units
