Question

The area of a bulletin board is 52 square feet the length is three feet less than four times the width find the length and width of the bulletin board

Answer 1

The length of the bulletin board is 13\ ft
The width of the bulletin board is 4\ ft

Answer 2

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 $4w-3$.

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:

$w(4w-3)=52$

Let us solve for w.

$w(4w-3)=52$

$4w^2-3w=52$  

Use quadratic formula:

$w=\frac{-(-3)\pm\sqrt{(-3)^3-4\cdot 4\cdot (-52)}}{2\cdot 4}$

$w=\frac{3\pm\sqrt{9+832}}{8}$

$w=\frac{3\pm\sqrt{841}}{8}$

$w=\frac{3\pm29}{8}$

$w=\frac{3-29}{8}\text{ (or) }w=\frac{3+29}{8}$

$w=\frac{-26}{8}\text{ (or) }w=\frac{32}{8}$

$w=\frac{-13}{4}\text{ (or) }w=4$

Since width cannot be negative, therefore, width of the bulletin board is 4 feet.

Substitute $w=4$ in expression $4w-3$ to find length of bulletin board.

$4w-3\Rightarrow 4(4)-3=16-3=13$

Therefore, length of the bulletin board is 13 feet.