Explanation:

- Given Data:

- Perimeter of rectangle = 94 m

- Area of rectangle = 420 m²

- Let:

- Length = l

- Width = w

- Formulate Equations:

- $2(l+w)=94$, which simplifies to $l+w=47$.

- $l\times w=420$.

- Solve for Dimensions:

- Use the system of equations:

- $l+w=47$

- $lw=420$

- Solving gives: $l=35$, $w=12$ (or vice versa).

- Calculate Diagonal:

- Diagonal, $d=\sqrt{l^2+w^2}$

- $d=\sqrt{{35}^2+{12}^2}=\sqrt{1225+144}=\sqrt{1369}=37$ m

- Options:

- Option 1: 32 m

- Option 2: 36 m

- Option 3: 35 m

- Option 4: 37 m

- Conclusion:

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