Question

1. math on the spot a nursery manager is buying fencing to enclose three sides of a garden, with two short sides and one long side. the garden is a rectangle with sides 2x and 3x, where x is feet. the area of the garden is 3000 square feet. the manager can buy fencing in whole feet only. how many feet of fencing should he buy?

Explanation:

Step1: Find the value of x

The area of a rectangle is $A = l\times w$. Here, $A = 3000$, $l = 3x$ and $w = 2x$. So, $3x\times2x=3000$, which simplifies to $6x^{2}=3000$. Then $x^{2}=\frac{3000}{6}=500$, and $x=\sqrt{500}\approx22.36$.

Step2: Determine the sides of the rectangle

The two - short sides are of length $2x$ and the long side is of length $3x$. The two short - side lengths are $2x$ each and one long - side length is $3x$. The total length of the fencing $L = 2(2x)+3x=4x + 3x=7x$.

Step3: Calculate the length of the fencing

Substitute $x=\sqrt{500}$ into $L = 7x$. So, $L = 7\sqrt{500}\approx7\times22.36 = 156.52$. Since the manager can buy fencing in whole feet only, we round up to 157 feet.

Answer:

157