Answer:
The length of the unknown side is 10 meters
Explanation:
we know that
In this problem we have an isosceles right triangle
Applying the Pythagorean Theorem
![c^2=a^2+b^2](https://img.qammunity.org/2021/formulas/mathematics/middle-school/byhrr90olo1xo4n215kg0bc367cjwlvx2c.png)
where
c is the hypotenuse (unknown side)
a and b are the legs
we have
![a=7\ m\\b=7\ m](https://img.qammunity.org/2021/formulas/mathematics/middle-school/xpa5dqtyi41cxv6kb10ezgx1tto0zhyy5d.png)
substitute
![c^2=7^2+7^2](https://img.qammunity.org/2021/formulas/mathematics/middle-school/ynst0cuza31c475dayh5wnc8g9v2gjjpn9.png)
![c^2=(2)7^2](https://img.qammunity.org/2021/formulas/mathematics/middle-school/ykz66teur5g0gedzocqin44er849a2cu6u.png)
![c=7√(2)\ m](https://img.qammunity.org/2021/formulas/mathematics/middle-school/ebdf3f89to5vzdbt5u7jg63mhwb6bq5myt.png)
![c=9.9\ m](https://img.qammunity.org/2021/formulas/mathematics/middle-school/wotbigaxs4qcrdqxqo9q0or4j04kc53qkb.png)
Round to the nearest whole number
![c=10\ m](https://img.qammunity.org/2021/formulas/mathematics/middle-school/zz19j11pke4406kgu6zdjwo4k9ys89i5nk.png)
therefore
The length of the unknown side is 10 meters