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Sagot :
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given information
[tex]\begin{gathered} Perimeter=2l+2b=28m \\ Area=lb=45m^2 \\ \\ where\text{ l is the length, b is the breadth} \end{gathered}[/tex]STEP 2: Label the two equations
[tex]\begin{gathered} 2l+2b=28------equation\text{ 1} \\ lb=45----equation\text{ 2} \end{gathered}[/tex]STEP 3: Solve for the missing values
Isolate l in equation 1
[tex]\begin{gathered} 2(l+b)=28 \\ l+b=\frac{28}{2}=14 \\ l=14-b-----equation\text{ 3} \end{gathered}[/tex]Substitute 14-b for l in equation 2
[tex]\begin{gathered} (14-b)\cdot b=45 \\ 14b-b^2=45 \\ We\text{ have the quadratic equation} \\ -b^2+14b-45=0 \end{gathered}[/tex]Solve the equation quadratically
[tex]\begin{gathered} -b^{2}+14b-45=0 \\ -b^2+9b+5b-45=0 \\ -b(b-9)+5(b-9)=0 \\ (-b+5)(b-9)=0 \\ -b+5=0,b=5 \\ b-9=0,b=9 \\ \\ b=5,b=9 \end{gathered}[/tex]Substitute the values into equation 3,
[tex]\begin{gathered} l=14-b \\ when\text{ b = 5} \\ l=14-5=9 \\ When\text{ b = 9} \\ l=14-9=5 \end{gathered}[/tex]Hence, the dimensions of the pen is given as:
[tex]9m\text{ }by\text{ }5m[/tex]
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