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 Fence
The 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]
