Question

q15: i want to build a rectangular fence around my yard. the length of my yard is 52 and 3/4 feet and the width is 19 and 3/16 feet. how much fencing will i need? a. 71 and 3/4 ft b. 33 and 3/8 ft c. 143 and 7/8 ft

Explanation:

Step1: Convert mixed - numbers to improper fractions

The length $l = 52\frac{3}{4}=\frac{52\times4 + 3}{4}=\frac{208+3}{4}=\frac{211}{4}$ feet, and the width $w=19\frac{3}{16}=\frac{19\times16 + 3}{16}=\frac{304 + 3}{16}=\frac{307}{16}$ feet.

Step2: Recall the perimeter formula for a rectangle

The perimeter $P$ of a rectangle is $P = 2(l + w)$.

Step3: Add the length and width

First, find a common denominator for $l$ and $w$. The common denominator of 4 and 16 is 16. So, $\frac{211}{4}=\frac{211\times4}{4\times4}=\frac{844}{16}$. Then $l + w=\frac{844}{16}+\frac{307}{16}=\frac{844 + 307}{16}=\frac{1151}{16}$ feet.

Step4: Calculate the perimeter

$P = 2\times\frac{1151}{16}=\frac{1151}{8}=143\frac{7}{8}$ feet.

Answer:

C. 143 and 7/8 ft