Answer:
![x=6.5\ units](https://img.qammunity.org/2020/formulas/mathematics/middle-school/6t51vaetzjyc897g5xikb0zh0g6w2nl8ug.png)
Explanation:
step 1
Find the length side of the smaller square
The area of the square is equal to
![A=a^(2)](https://img.qammunity.org/2020/formulas/mathematics/middle-school/7sc96f9f6vc3rxbpb4sw3pcumvvtig5fwd.png)
so
![a^(2)=13](https://img.qammunity.org/2020/formulas/mathematics/middle-school/bub2jn9ortl70726ezxuyuvy43z6qr7dpx.png)
![a=√(13)\ units](https://img.qammunity.org/2020/formulas/mathematics/middle-school/p2pytfnxt2boae2jd7fbxkosuw8mvww8n5.png)
step 2
Find the length side of the larger square
The area of the square is equal to
![A=b^(2)](https://img.qammunity.org/2020/formulas/mathematics/middle-school/z7z681nqfs0ruu0905ybb033ebqg24se8n.png)
so
![b^(2)=29.25](https://img.qammunity.org/2020/formulas/mathematics/middle-school/7h8zk7hzhc1ebvm6g7d8yc6bvmkcafbkb9.png)
![b=√(29.25)\ units](https://img.qammunity.org/2020/formulas/mathematics/middle-school/ms33j80v45o5ldz4wmkzv98lu2rbelmq8m.png)
step 3
Find the value of x
Applying the Pythagoras Theorem
![x^(2) =a^(2)+b^(2)](https://img.qammunity.org/2020/formulas/mathematics/middle-school/wvl086n59dtreek1hf1ryqliclo5srixxb.png)
substitute the values
![x^(2) =13+29.25](https://img.qammunity.org/2020/formulas/mathematics/middle-school/50hcku480cpmtp030tdq6vh91qo29gzxle.png)
![x^(2) =42.25](https://img.qammunity.org/2020/formulas/mathematics/middle-school/90fjvbm6fnfo14rpjkj71z8tnrva4cmz13.png)
![x=6.5\ units](https://img.qammunity.org/2020/formulas/mathematics/middle-school/6t51vaetzjyc897g5xikb0zh0g6w2nl8ug.png)