Q53. - Algebra 2

Question

If the perimeter of the square shown at the right is $48 units$, find the value of x.

$\begin{array}{l}A.3\\ B.4\\ C.6\\ D.8\end{array}$

Step-by-Step Solution

Answer

The value of x is Option A $3$.

Step-1 – Apply the concept of perimeter of square

All sides of a square are equal. The perimeter of a square with side a is equal to the sum of all side which is mathematically expressed as.

$\begin{array}{c}P=a+a+a+a\\ P=4a\end{array}$

Step-2 – Description of step

Since all sides of a square are equal, and it is given that measurement of one side is 2y and other side is 4x. so equating both the sides and simplify the equation as shown

$\begin{array}{c}2y=4x\\ y=2x\end{array}$

Step-3 – Description of step

It is given that perimeter of the square is $48 units$. So, apply the formula of finding the perimeter with side 4x as all sides are equal and find the value of x

$\begin{array}{c}P=a+a+a+a\\ 48=2y+4x+2y+4x\\ 48=4y+8x\\ 12=y+2x\end{array}$

Now, substitute the value of $y=2x$ in $12=y+2x$ and solve to find the value of x.

$\begin{array}{c}y+2x=12\\ 2x+2x=12\\ 4x=12\\ x=3\end{array}$

Thus, the value of x is 3.

Hence, value of x is $3$ and the correct option is Option C.