All categories

2 years ago

Among all rectangles having a perimeter of 25m, find the dimensions of the one with the largest area

Mathematics

2 answers:

Katen [24]2 years ago

7 0

Answer:

Square with side length 25/4 m

Step-by-step explanation:

The area is always going to be largest for a rectangle when the two dimensions are equal. You are looking for a square. What square has perimeter 25? 4s=25 so the side length of this rectangle (Square) is 25/4 m.

Alchen [17]2 years ago

3 0

Answer:

It's a square 6.25 * 6.25 m.

Step-by-step explanation:

We can do this using calculus.

Let the length of the rectangle be x m.

2x + 2w = 25 where w = the width.

2w = 25 - 2x

w = 12.5 - x

So the area A = x(12.5 - x) = 12.5x - x^2.

Finding the derivative:

dA /dx = 12.5 - 2x

For a maximum area this = zero

12.5 - 2x = 0

x = 6.25m.

and w = 25 - 12.5 = 6.25m.

(For any rectangle the maximum area is always a square).

You might be interested in

Javier is considering two lawn care services. Premier Landscaping charges $15.00 for travel to the job site and $55.00 per hour

Wittaler [7]

Answer:

Time in which both companies charge same cost = 1.5 hour

Step-by-step explanation:

Given:

Fixed Variable

Premier Landscaping charges $15 $55

Ace Landscaping charges $65

Find:

Time in which both companies charge same cost:

Computation:

Assume in X time both companies charge same cost:

So,

Premier Landscaping total cost = Ace Landscaping total cost

⇒ $15 + $55(Time taken) = $65 (Time taken)

⇒ $15 = $65 (Time taken) - $55(Time taken)

⇒ $15 = $10 (Time taken)

⇒ Time taken = 1.5 hour

Time in which both companies charge same cost = 1.5 hour

6 0

3 years ago

In the diagram, point D divides line segment AB in the ratio of 5:3. If line segment AC is vertical and line segment CD is horiz

BabaBlast [244]

Answer:

C (2, -1)

Step-by-step explanation:

C has the same x coordinate as A = 2

that eliminates A and B.

and the y value of C has to be closer to the y value of B than to the y value of A (due to the 5:3 ratio).

so, without spending unnecessary effort on actual calculation, we can directly derive the correct answer to be C.

but to show in numbers, the "coordinate triangle" of the difference between D and B is a similar triangle to ACD. and so, the ratio of one side pair applies then to all other sides too. including the individual coordinate differences.

so, also the y difference of A to D relates to the y difference between D and B in the same ratio of 5:3 of the overall y difference of A to B.

the y difference A to B is 2 - -6 = 8

the 5/3 split of 8 units is actually 5 and 3.

so, the y coordinate of D is -6 + 5 = -1

and C must have the same y coordinate.

therefore, it is proven that answer C (2, -1) is the right answer.

4 0

2 years ago

On your wedding day you leave for the church 34 minutes before the ceremony is to begin, which should be plenty of time since th

Schach [20]

Answer:

Average speed is 37.35 mi/h