Answer:
[tex]g=28.8\ units[/tex]
Step-by-step explanation:
see the attached figure with letters to better understand the problem
step 1
In the right triangle BDC
Find the value of j
Applying the Pythagorean Theorem
[tex]j^2=5^2+12^2[/tex]
[tex]j^2=169\\j=13\ units[/tex]
step 2
In the right triangle ABD
Applying the Pythagorean Theorem
[tex]h^2=12^2+g^2[/tex] ----> equation A
step 3
In the right triangle ABC
Applying the Pythagorean Theorem
[tex](g+5)^2=h^2+13^2[/tex] ----> equation B
step 4
Substitute equation A in equation B
[tex](g+5)^2=(12^2+g^2)+13^2[/tex]
solve for g
[tex]g^2+10g+25=144+g^2+169\\10g=288\\g=28.8\ units[/tex]
