We can use a diagram to show the backyard:
The length of the diagonal can be gotten using the Pythagorean Theorem given to be:
![c^2=a^2+b^2](https://img.qammunity.org/2023/formulas/mathematics/high-school/udh1dsx7kwgfauditnn86pp2qhoycm1tvv.png)
where c is the length of the hypotenuse and a and b are the other two sides.
Therefore, we can calculate the length of the hypotenuse to be:
![\begin{gathered} x^2=24^2+45^2 \\ x^2=576+2025 \\ x^2=2601 \\ x=\sqrt[]{2601} \\ x=51 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/high-school/hz8rgbf7afbg8ev8xz4z1643z2hrovg9ju.png)
The length of the chicken wire fence will be 51 m.