ANSWER:
(a)
[tex]W^{2}+4W-525=0[/tex]
(b)
Width: 21 feet
Length: 25 feet
STEP-BY-STEP EXPLANATION:
Given:
Width (W) = W ft
Length (L) = (4 + W) ft
Area (A) = 525 ft^2
(a)
The area of a rectangle is equal to the product of its length and width, therefore:
[tex]\begin{gathered} A=L\cdot W \\ \\ \text{ We replacing} \\ \\ 525=(4+W)\cdot(W) \\ \\ 4W+W^2=525 \\ \\ W^2+4W-525=0 \end{gathered}[/tex]
(b)
We solve the equation by factoring:
[tex]\begin{gathered} W^{2}+4W-525=0 \\ \\ 4W=-21W+25W \\ \\ W^2-21W+25W-525=0 \\ \\ W(W-21)+25(W-21)=0 \\ \\ (W-21)(W-25)=0 \\ \\ W-21=0\rightarrow W=21 \\ \\ W+25=0\rightarrow W=-25 \end{gathered}[/tex]
The width of the rectangle is equal to 21 feet and the length of the rectangle is equal to 25 feet.
