Answer:
[tex]x=6.5\ units[/tex]
Step-by-step explanation:
step 1
Find the length side of the smaller square
The area of the square is equal to
[tex]A=a^{2}[/tex]
so
[tex]a^{2}=13[/tex]
[tex]a=\sqrt{13}\ units[/tex]
step 2
Find the length side of the larger square
The area of the square is equal to
[tex]A=b^{2}[/tex]
so
[tex]b^{2}=29.25[/tex]
[tex]b=\sqrt{29.25}\ units[/tex]
step 3
Find the value of x
Applying the Pythagoras Theorem
[tex]x^{2} =a^{2}+b^{2}[/tex]
substitute the values
[tex]x^{2} =13+29.25[/tex]
[tex]x^{2} =42.25[/tex]
[tex]x=6.5\ units[/tex]
