Question

A rectangular garden is 20ft longer than it is wide. It’s area is 6300ft^2. What are its dimensions

Answer 1

Answer:

Length = 90 feet

Width = 70 feet

Step-by-step explanation:

    The area of a rectangle is found by finding the product of the length. Therefore, the following formula equation can be made:

$A=lw$

    The problem tells us that the area of the garden is 6,300 square feet and that the length is 20 feet longer than the width. Therefore, our equation can be rewritten as such:

$6300=(w+20)(w)~or~6300=w(w+20)$

Now that there are no longer two different variables, we can solve for w.

$6300=w(w+20)\\\\6300=w^2+20w\\\\0=w^2+20w-6300$

    We are left with a trinomial so we'll use the quadratic formula to further solve for w.

$w=\frac{-20\pm\sqrt{20^2-4(1)(-6300)} }{2(1)}\\\\w=\frac{-20\pm\sqrt{400+25200} }{2}\\\\w=\frac{-20\pm\sqrt{25600} }{2}\\\\w=\frac{-20\pm160}{2}\\\\\\w=70\\or\\w=-90$

    Since distance cannot be negative, w = -90 cannot be a solution for this problem. Therefore, the width of the rectangular garden is 70 feet.

    Now that the width has been found, we know the length is 20 feet longer than it. Therefore, the length is 90 feet.