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The perimeter of a rectangle is 32 meters and the length is 4 meters longer than width

The perimeter of a rectangle is 32 meters and the length is 4 meters longer than width-example-1

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Given:

The perimeter of a rectangle is 32 meters and the length is 4 meters longer than the width

Let, x = the length of the rectangle

And, y = the width of the rectangle

So, we have the following system of equations:


\begin{gathered} 2x+2y=32\rightarrow(1) \\ x-y=4\rightarrow(2) \end{gathered}

We will use the method of substitution to solve the system

So, from equation 2:


x=y+4\rightarrow(3)

substitute with (x) from equation (3) intp eqaution (1)


2(y+4)+2y=32

solve the equation to find (y):


\begin{gathered} 2y+8+2y=32 \\ 4y+8=32 \\ 4y=32-8 \\ 4y=24 \\ y=(24)/(4)=6 \end{gathered}

Now, substitute with (y) into equation (3) to find (x):


x=y+4=6+4=10

So, the answer will be:

The length of the rectangle = 10 m

The width of the rectangle = 6 m

User Sophie Swett
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