A rectangle has area 64 m2. Express the perimeter of the rectangle as a function of the length L of one of its sides.

State the domain of P. (Assume the length of the rectangle is larger than its width. Enter your answer using interval notation.)

damon smd

ur bad at explaining

Ah, the mystery of the rectangular riddle! Let's humorously unravel it, shall we?

To express the perimeter (P) of the rectangle as a function of the length (L) of one of its sides, we need to crack the code of its sides.

We know that the area (A) of a rectangle is equal to its length (L) multiplied by its width (W). In this case, the area is 64 m². So, we can write the equation as L * W = 64.

Now, since we're only dealing with one side here, let's assume the other side is the width (W). This means L * W = 64.

To express the perimeter, we need to add up the lengths of all sides. In this case, we have two identical sides with lengths L, and two identical sides with lengths W. So the perimeter P is given by P = 2L + 2W = 2L + 2(L * W)/L.

But we know that L * W = 64, so we can substitute that in: P = 2L + 2(64)/L.

Now, let's simplify this expression a bit: P = 2L + 128/L.

So, the perimeter P of the rectangle is a function of the length L, expressed by P = 2L + 128/L. Ta-da!

As for the domain of P, we need to consider the restrictions. In this case, the length L of the rectangle needs to be larger than its width. Since the sides cannot be negative or zero, we can say that the domain of P is all positive values of L excluding L = 0.

Therefore, the domain of P in interval notation is (0, ∞). Keep on laughing and calculating!

good

To find the perimeter of a rectangle, we need to know the lengths of both sides of the rectangle. Let's assume the length of one side of the rectangle is L, and the width is W.

We know that the area of a rectangle is given by the formula: Area = Length × Width.

In this case, we are given that the area is 64 m^2, so we can write the equation: 64 = L × W.

However, we are only asked to express the perimeter (P) of the rectangle as a function of the length (L) of one of its sides. The perimeter (P) of a rectangle is given by the formula: Perimeter = 2 × (Length + Width).

Since we're expressing the perimeter as a function of L, we need to eliminate W from the equation. To do that, we solve the equation 64 = L × W for W, and substitute the value into the perimeter formula:

W = 64/L

Perimeter = 2 × (L + 64/L)

So, the perimeter of the rectangle as a function of the length (L) of one of its sides is: P(L) = 2(L + 64/L).

Now let's determine the domain of P.

Since the length (L) of the rectangle is given to be larger than its width, it means L > W. Substituting the value of W we found, it means L > 64/L.

If we multiply both sides of the inequality by L, we get L^2 > 64.

Taking the square root of both sides (remembering to consider both the positive and negative square roots), we get L > 8 and L < -8. But since the length cannot be negative in this context, we have L > 8.

Therefore, the domain of P is L > 8.

Expressed in interval notation, the domain of P is (8, ∞).

What are the answers for the quick check

p = 2L + 2 w

w = 64/L
so
p = 2L +128/L

w can range from 0 to L
if w = 0, L ---->oo and p -->oo
if w = L, L = w =8 and p = 4*8 = 32
so
32 </= p </= oo