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

Answer:

(a)The missing measurements are 9 feet and $16\frac{1}{4} feet$.

(b)Therefore, the length of the fence is  $97\frac{1}{2} feet$

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:

$y+8\frac{1}{4}=17 \frac{1}{4}\\y=17 \frac{1}{4}-8\frac{1}{4}\\y=9 feet$

Similarly:

$x+15\frac{1}{4}=31\frac{1}{2}\\x=31\frac{1}{2}-15\frac{1}{4}\\x=31-15+\frac{1}{2}-\frac{1}{4}\\x=16+\frac{1}{4}\\x=16\frac{1}{4} feet$

The missing measurements are 9 feet and $16\frac{1}{4} feet$.

(b)Length of the Fence

The fence is rectangular shaped with:

Length = $31\frac{1}{2} feet$

Width = $17 \frac{1}{4} feet$

Perimeter of a Rectangle = 2(L+W)

Therefore, the length of the fence

$=2(31\frac{1}{2}+17 \frac{1}{4})\\=2(31+17+\frac{1}{2}+ \frac{1}{4})\\=2(48+ \frac{3}{4})\\=96+\frac{3}{2}\\=97\frac{1}{2} feet$