



 
Hi Lucy, I am going to start with a diagram. I let L feet be the length of the entire yard. The area of the garden is $18 \times 51 = 918$ square feet and you are told that this is $24 \%$ of the area of the entire back yard. Suppose that the area of the back yard is $x$ square feet then the garden area, 918 square feet, is $24 \%$ of $x.$ That is \[918 = 0.24 \times x.\] Solve for $x$ by dividing both side by 0.24 to get \[x = \frac{918}{0.24} = 3825 \mbox{ square feet.}\] From the diagram the area of the back yard is $51 \times L$ square feet and hence \[51 \times L = 3825 \mbox{ square feet.}\] This time solve for $L$ by dividing both sides by 51 to get \[L = \frac{3825}{51} = 75 \mbox{ feet.}\] I hope this helps,  


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