Answer :
Answer
Length = 10 ft
Width = 5 ft
Explanation
Area of the rectangle given = 50 ft²
Let the width of the rectangle be x
So this means the length of the rectangle will be 3x - 5
What to find:
The dimensions of the rectangle.
Step-by-step solution:
Area of a rectangle = length x width
i.e A = L x W
Put A = 50, L = 3x - 5, W = x into the formula.
[tex]\begin{gathered} 50=(3x-5)x \\ 50=3x^2-5x \\ 3x^2-5x-50=0 \end{gathered}[/tex]The quadratic equation can now be solve using factorization method:
[tex]\begin{gathered} 3x^2-5x-50=0 \\ 3x^2-15x+10x-50=0 \\ 3x(x-5)+10(x-5)=0 \\ (3x+10)(x-5)=0 \\ 3x+10=0\text{ }or\text{ }x-5=0 \\ 3x=-10\text{ }or\text{ }x=5 \\ x=-\frac{10}{3}\text{ }or\text{ }x=5 \end{gathered}[/tex]Since the dimension can not be negative, hence the value of x will be = 5.
Therefore, the dimensions of the rectangle will be:
[tex]\begin{gathered} Length=3x-5=3(5)-5=15-5=10\text{ }ft \\ \\ Width=x=5\text{ }ft \end{gathered}[/tex]