Question

Jim's backyard is a rectangle that is 15 5/6 yards long and 10 2/5 yards wide. Jim buys sod in pieces that are 1 1/3 yards long and 1 1/3 yards wide how many pieces of sod will Jim need to buy to cover his backyard with sod

Answer 1

Answer:

93 pieces

Step-by-step explanation:

To cover his backyard with sod, he needs to cover the area of the backyard.

His backyard is a rectangle, and area of a rectangle is given as:

$A=lw$

Where,

$l$ is the length, and

$w$ is the width

So, the area of Jim's backyard is $l*w=15\frac{5}{6}*10\frac{2}{5}=\frac{95}{6}*\frac{52}{5}=\frac{494}{3}$ square yards.

The area of each sods are solved using the area of the rectangle formula. So we have $l*w=1\frac{1}{3}*1\frac{1}{3}=\frac{4}{3}*\frac{4}{3}=\frac{16}{9}$ square yards as the area of each sod.

To find HOW MANY of these sods we would need to cover the whole backyard, we divide the backyard area by each sod area:

$\frac{\frac{494}{3}}{\frac{16}{9}}=\frac{741}{8}=92.625$

Since, fractional sods can't be bought, Jim has to buy 93 sods to cover his backyard.

Answer 2

By definition, the area of a rectangle is given by:
 $A = (w) * (l)$
 Where,
 w: width of the rectangle
 l: length of the rectangle
 Substituting values we have:
 $A = (10 \frac{2}{5} ) * (15 \frac{5}{6}) A = 164.7$
 Then, the area of each piece of sod is:
 $A = (1 \frac{1}{3} ) * (1 \frac{1}{3}) A = 1.8$
 Thus, the number of pieces is given by the division of both areas:
 $N = (164.7) / (1.8) N = 91.5$
 Rounding the nearest whole we have:
 $N = 92$
 Answer:
 Jim will need to buy 92 pieces of sod to cover his backyard