Dante's Mom wants to build a fence around their yard. Here are the measurements of the yard. What are the measurements of the missing side of the yard? How long will the fence be.
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Question:
Dante's Mom wants to build a fence around their yard. Here are the measurements of the yard. What are the measurements of the missing side of the yard? How long will the fence be.
Answers
Answer:(a)The missing measurements are 9 feet and [tex]16\frac{1}{4}$ feet[/tex].(b)Therefore, the length of the fence is [tex]97\frac{1}{2}$ feet[/tex]Step-by-step explanation:The diagram of the yard is attached below.(a)I have labeled the missing dimensions of the yard as x and y.Therefore:[tex]y+8\frac{1}{4}=17 \frac{1}{4}\\y=17 \frac{1}{4}-8\frac{1}{4}\\y=9$ feet[/tex]Similarly:[tex]x+15\frac{1}{4}=31\frac{1}{2}\\x=31\frac{1}{2}-15\frac{1}{4}\\x=31-15+\frac{1}{2}-\frac{1}{4}\\x=16+\frac{1}{4}\\x=16\frac{1}{4}$ feet[/tex]The missing measurements are 9 feet and [tex]16\frac{1}{4}$ feet[/tex].(b)Length of the FenceThe fence is rectangular shaped with:Length = [tex]31\frac{1}{2}$ feet[/tex]Width = [tex]17 \frac{1}{4}$ feet[/tex]Perimeter of a Rectangle = 2(L+W)Therefore, the length of the fence [tex]=2(31\frac{1}{2}+17 \frac{1}{4})\\=2(31+17+\frac{1}{2}+ \frac{1}{4})\\=2(48+ \frac{3}{4})\\=96+\frac{3}{2}\\=97\frac{1}{2}$ feet[/tex]
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