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4 years ago

What is the perimeter

Mathematics

2 answers:

Sidana [21]4 years ago

8 0

Um, we see this as a composite figure. We just need to separate this into shapes. And if we separate this composite figure, it will have three shapes- triangle, square and semi-circle
Triangle:
To finds its perimeter, add 3 sides together:
We know that its base is 6 unit, and the height is 3 unit, divided this triangle into half, and to find the side, use Pythagorean theorem:
a^2+b^2=c^2
6^2+3^2=c^2
36+9=c^2
45=c^2
Square root
c≈6.71 unit
P≈6.71+6.71+4
P≈17.42 unit
Square:
2+2=4 unit, because we just need to calculate the outsude layer
Semi-circle:
C=πd, let π represent 3.14
Where
d=6 unit
C=6×3.14
C=18.84 unit. However, this is the perimeter of the whole circle, so
Perimeter of the semi-circle=
18.84/2=9.42 unit.
As a result, the perimeter of the composite figure:
17.42+4+9.42=30.84 units. Hope it help!

german4 years ago

3 0

Its about 19.2 I'm pretty sure

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3 years ago

A piece of wire 11 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral tria

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11 meters

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First, we can say that the square has a side length of x. The perimeter of the square is 4x, and that is how much wire goes into the square. To maximize the area, we should use all the wire possible, so the remaining wire goes into the triangle, or (11-4x).

The area of the square is x², and the area of an equilateral triangle with side length a is (√3/4)a². Next, 11-4x is equal to the perimeter of the triangle, and since it is equilateral, each side has (11-4x)/3 length. Plugging that in for a, we get the area of the equilateral triangle is

(√3/4)((11-4x)/3)²

= (√3/4)(11/3 - 4x/3)²

= (√3/4)(121/9 - 88x/9 + 16x²/9)

= (16√3/36)x² - (88√3/36)x + (121√3/36)

The total area is then

(16√3/36)x² - (88√3/36)x + (121√3/36) + x²

= (16√3/36 + 1)x² - (88√3/36)x + (121√3/36)

Because the coefficient for x² is positive, the parabola would open up and the derivative of the parabola would be the local minimum. Therefore, to find the maximum area, we need to go to the absolute minimum/maximum points of x (x=0 or x=2.75)

When x=0, each side of the triangle is 11/3 meters long and its area is

(√3/4)a² ≈ 5.82

When x=2.75, each side of the square is 2.75 meters long and its area is

2.75² = 7.5625

Therefore, a maximum is reached when x=2.75, or the wire used for the square is 2.75 * 4 = 11 meters

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3 years ago