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.

Answer 1

(a)The missing measurements are 9 feet and
`16(1)/(4)$ feet`.

(b)Therefore, the length of the fence is
`97(1)/(2)$ feet`

Explanation:

The diagram of the yard is attached below.

(a)I have labeled the missing dimensions of the yard as x and y.

Therefore:

`y+8(1)/(4)=17 (1)/(4)\\y=17 (1)/(4)-8(1)/(4)\\y=9$ feet`

Similarly:

`x+15(1)/(4)=31(1)/(2)\\x=31(1)/(2)-15(1)/(4)\\x=31-15+(1)/(2)-(1)/(4)\\x=16+(1)/(4)\\x=16(1)/(4)$ feet`

The missing measurements are 9 feet and
`16(1)/(4)$ feet`.

(b)Length of the Fence

The fence is rectangular shaped with:

Length =
`31(1)/(2)$ feet`

Width =
`17 (1)/(4)$ feet`

Perimeter of a Rectangle = 2(L+W)

Therefore, the length of the fence

`=2(31(1)/(2)+17 (1)/(4))\\=2(31+17+(1)/(2)+ (1)/(4))\\=2(48+ (3)/(4))\\=96+(3)/(2)\\=97(1)/(2)$ feet`