Answer
Length $=12$ feet.
Width $=5$ feet.
Work Step by Step
Step 1:- Assume unknown quantities as variables.
Let the length of the rectangle be $=x$.
Let the width of the rectangle be $=y$.
Step 2:- Write the system of equations.
Perimeter of the rectangular tabletop $=34$ feet.
$4$ times the length minus $3$ times the width is equal to $33$ feet.
The formula for the perimeter of the rectangle is
$=2(length+width)$.
Or we can write.
$\Rightarrow 2(x+y)=34$ ...... (1)
$\Rightarrow 4x-3y=33$...... (2)
Step 3:- Solve the system of equations.
Divide the equation (1) by $2$ and multiply by $3$.
$\Rightarrow 3x+3y=51$ ...... (3)
Add equation (2) and (3).
$\Rightarrow 4x-3y+3x+3y=33+51$
Simplify.
$\Rightarrow 7x=84$
Divide both sides by $7$.
$\Rightarrow \frac{7x}{7}=\frac{84}{7}$
Simplify.
$\Rightarrow x=12$
Plug the value of $x$ into equation (3).
$\Rightarrow 3(12)+3y=51$
Isolate $y$.
$\Rightarrow y=\frac{51-36}{3}$
Simplify.
$\Rightarrow y=5$.
Step 4:- Check the answers.
Substitute the values of $x$ and $y$ into equation (1).
$\Rightarrow 2(12+5)=34$
$\Rightarrow 2(17)=34$
$\Rightarrow 34=34$ True.
