Question

nikkis backyard is in the shape of a rectangle. the length is 27 feet. the width is one - third the length plus 4 feet. write and evaluate an expression to find the area of nikkis backyard.
a. $27\times2 + 2\times(\frac{1}{3}\times27 + 4)$
b. $27\times(\frac{1}{3}\times27 + 4)$
c. $(27\times\frac{1}{3})\times27 + 4$
d. $(2\times27)\times(2\times\frac{1}{3}\times27 + 4)$
evaluate the expression to find the area of nikkis backyard. the area of nikkis backyard is square feet.

Explanation:

Step1: Find the width

The length $l = 27$ feet. The width $w=\frac{1}{3}\times l + 4$. Substituting $l = 27$ into the width - formula, we get $w=\frac{1}{3}\times27 + 4$.
$w=\frac{1}{3}\times27+4=9 + 4=13$ feet.

Step2: Find the area formula

The area formula for a rectangle is $A=l\times w$. Here, $l = 27$ and $w = 13$, and the correct expression for the area is $A = 27\times(\frac{1}{3}\times27 + 4)$.

Step3: Evaluate the expression

First, calculate the value inside the parentheses: $\frac{1}{3}\times27+4=9 + 4=13$.
Then, multiply by the length: $27\times13 = 351$ square - feet.

Answer:

B. $27\times(\frac{1}{3}\times27 + 4)$; 351 square feet