Question

A rectangular garden is 5 ft longer than it is wide. Its area is 1800ft^2. What are its dimensions?

Answer 1

Answer:

The dimensions are 45 feet by 40 feet.

Step-by-step explanation:

Recall that the area of a rectangle is given by:

$\displaystyle A=w\ell$

Where w is the width and l is the length.

The length is five feet longer than the width. Thus, we can write that:

$\ell = w+5$

The total area is 1800 square feet. Substitute:

$1800=w(w+5)$

Solve for w. Distribute:

$w^2+5w=1800$

Subtract 1800 from both sides:

$w^2+5w-1800=0$

Factor. We can use 45 and -40. Hence:

$\displaystyle (w+45)(w-40)=0$

Zero Product Property:

$w+45=0\text{ or } w-40=0$

Solve for each case:

$\displaystyle w=-45\text{ or } w=40$

Since the width cannot be negative, we can ignore the first solution.

So, the width is 40 feet. Since the length is five feet longer, the length is 45 feet.

The dimensions are 45 feet by 40 feet.