Answer :
Answer:
Length = 13 units
width = 2 units
Explanations:
The formula for calculating the area of a rectangle is given as:
[tex]A=lw[/tex]where:
l is the length of the rectangle
w is the width of the rectangle
If the width of a rectangle is 11 units less than the length, then;
[tex]w=l-11[/tex]Substitute the expression for the width and the area into the formula for calculating the area.
[tex]\begin{gathered} 26=l(l-11) \\ 26=l^2-11l \\ l^2-11l-26=0 \end{gathered}[/tex]Factorize the resulting quadratic expression
[tex]\begin{gathered} l^2-13l+2l-26=0 \\ l(l-13)+2(l-13)=0 \\ (l+2)(l-13)=0 \end{gathered}[/tex]Find the length
[tex]\begin{gathered} l-13=0 \\ l=13units \end{gathered}[/tex]Recall that A = lw, hence;
[tex]\begin{gathered} w=\frac{A}{l} \\ w=\frac{26}{13} \\ w=2units \end{gathered}[/tex]Hence the dimensions of the rectangle is 13 units by 2 units