Answer:
Length: 13 feet,
Width: 4 feet.
Step-by-step explanation:
Let w represent width of bulletin board.
We have been given that the length is 3 feet less than 4 times the width. So the length of the bulletin board would be [tex]4w-3[/tex].
We have been given the area of a bulletin board is 52 square feet. We know that a bulletin board is in form of rectangle, so its area would be length times width.
We can represent this information in an equation as:
[tex]w(4w-3)=52[/tex]
Let us solve for w.
[tex]w(4w-3)=52[/tex]
[tex]4w^2-3w=52[/tex]
Use quadratic formula:
[tex]w=\frac{-(-3)\pm\sqrt{(-3)^3-4\cdot 4\cdot (-52)}}{2\cdot 4}[/tex]
[tex]w=\frac{3\pm\sqrt{9+832}}{8}[/tex]
[tex]w=\frac{3\pm\sqrt{841}}{8}[/tex]
[tex]w=\frac{3\pm29}{8}[/tex]
[tex]w=\frac{3-29}{8}\text{ (or) }w=\frac{3+29}{8}[/tex]
[tex]w=\frac{-26}{8}\text{ (or) }w=\frac{32}{8}[/tex]
[tex]w=\frac{-13}{4}\text{ (or) }w=4[/tex]
Since width cannot be negative, therefore, width of the bulletin board is 4 feet.
Substitute [tex]w=4[/tex] in expression [tex]4w-3[/tex] to find length of bulletin board.
[tex]4w-3\Rightarrow 4(4)-3=16-3=13[/tex]
Therefore, length of the bulletin board is 13 feet.
