Question

10 use the square figure given below to answer the following questions. (a) what is the perimeter of the square? (b) what is the area of the square?

Explanation:

Step1: Recall perimeter formula

The perimeter $P$ of a square with side - length $s$ is $P = 4s$. Here, $s=x + 3$.
$P=4(x + 3)$

Step2: Expand the expression

Using the distributive property $a(b + c)=ab+ac$, where $a = 4$, $b=x$, and $c = 3$.
$P=4x+12$

Step3: Recall area formula

The area $A$ of a square with side - length $s$ is $A=s^{2}$. Here, $s=x + 3$.
$A=(x + 3)^{2}$

Step4: Expand the area expression

Using the formula $(a + b)^{2}=a^{2}+2ab + b^{2}$, where $a=x$ and $b = 3$.
$A=x^{2}+6x + 9$

Answer:

(a) $4x + 12$
(b) $x^{2}+6x + 9$