Question

HELP ASAP!

Answer 1

Answer:

5.69 feet by 19.69 feet

Step-by-step explanation:

Given : A gardener wants to create a rectangular vegetable garden in a backyard. He wants it to have a total area of 112 square feet, and it should be 14 feet longer than it is wide.

Let x be the breadth of the rectangular vegetable garden

So, length of the rectangular vegetable garden  = ( x + 14 ) feet

To find: dimensions that a gardener should use for the vegetable garden

Solution :

We know that area of the rectangle is equal to length ( l ) × breadth ( b )

Area of the rectangular garden = 112 square feet

According to question,

$x(x+14)=112\Rightarrow x^2+14x-112=0$

In order to find roots, use quadratic formula which states that for equation $ax^2+bx+c=0$, roots are $\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Therefore, for equation $x^2+14x-112=0$, roots are $\frac{-14\pm \sqrt{196+448}}{2}=\frac{-14\pm \sqrt{644}}{2}$

Being a dimension, breadth can not be negative, so x = $\frac{-14- \sqrt{644}}{2}$ is rejected

Therefore,

$x=\frac{-14+ \sqrt{644}}{2}=5.69\Rightarrow l = x+14=5.69+14=19.69$

So, length = 19.69 feet and breadth = 5.69 feet

Answer 2

It is C because  5.69 multiplied by 19.69 equals 112.0361 Square Foot