Question

If $a$ is the length of a rectangle and $b$ is the breadth of the rectangle, then find $(Area{)}^m+(Perimeter{)}^n$ in terms of $a$ and $b$.

• A. $(a\times b{)}^n+(a+b{)}^n$
• B. $(a\times b{)}^m+(a+b{)}^m$
• C. $(a\times b{)}^m+2^n(a+b{)}^n$
• D. $(a+b{)}^m+(a+b{)}^n$

Answer 1

The correct option is C $(a\times b{)}^m+2^n(a+b{)}^n$

We are given with a rectangle of length $a$ and breadth $b$:


$\underset{–}{Step1:}$

Area of the rectangle $=length\times breadth$
$=a\times b$
$Area=a\times b$

Raising both the sides of the above equation to the power $m$:
$(Area{)}^m=(a\times b{)}^m$

$\underset{–}{Step2:}$

Perimeter of the rectangle $=2\times (length+breadth)$
$=2(a+b)$
$Perimeter=2(a+b)$

Raising both the sides of the above equation to the power $n$:
$(Perimeter{)}^n=[2(a+b){]}^n$
$=2^n(a+b{)}^n$


$\underset{–}{Step3:}$

$(Area{)}^m+(Perimeter{)}^n$
$=(a\times b{)}^m+2^n(a+b{)}^n$

The value of the expression $(Area{)}^m+(Perimeter{)}^n$ in terms of $a$ and $b$ is $(a\times b{)}^m+2^n(a+b{)}^n$. Therefore, option (c.) is the correct answer.