Question

.
If the area of a park is 24 sq m., then find the dimensions for the park which will have the least perimeter.

Answer 1

Answer:

The youth of the world is often the most ready to adapt to and learn to use new technologies, and they are certainly at the forefront of social media of all types. They have more technological know-how than many of older generations as well. Social media, therefore, is certainly having a rather large impact on their daily lives for good and for bad.

Those who spend too much time on social sites, or who take the abuses of online bullies seriously on the sites could have some issues. For parents, even those of teenagers who are 16 and 17, it is important to watch to make sure that social media sites do not take over the lives of children. When used appropriately, it can be a very good thing.

Answer 2

Step-by-step explanation:

Since, the word perimeter is used instead of circumference; so, I've considered the park to be non-circular; and a quadrilateral.

Let, length of the park = l metres.

So, breadth of the park = (24 / l) metres.

Perimeter of the park = P = 2 * {l + (24 / l)} metres.

Now, for optimum values (maximum or minimum) of P; dP / dl = 0.

Here, dP / dl = [2 * 1 + {48 * (-1) / (l^2)}] = 2 - {48 / (l^2)}.

When dP / dl = 0; 2 * (l^2) = 48; or, l = √24 = 2√6 ≈ 4.89898.

Now, d^2 P / dl^2 = 0 - {48 * (-2) / (l^3)} = {96 / (l^3)} > 0.

So, l ≈ 4.89898 stands for the minimum value of P.

So, for minimum perimeter b = (24 / l) = √24 ≈ 4.89898.

Therefore, perimeter of the park will be minimum when it will be square in shape having dimensions of (√24 metres * √24 metres) ≈ (4.89898 metres * 4.89898 metres).