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Ratling [72]
10 months ago
11

Suppose that a rectangle has a perimeter of 26 meters. Express the area A(x) of the rectangle in terms of the length x of one of

its sides. A(x)
Mathematics
1 answer:
ch4aika [34]10 months ago
4 0

The area A(x) of the rectangle in terms of the length x of one of its sides. A(x) = x(13-x).

<h3>What is rectangle?</h3>

A rectangle is really a closed two-dimensional geometry with four sides, four corners, and four right angles (90°). A rectangle's opposite sides are equal & parallel. Because  rectangles is a 2-D form, it has two dimensions: length and width.

Some characteristics of rectangle are-

  • The length of the rectangle is the longer side, while the width would be the shorter side.
  • Because all of the angles in a rectangle are equal, it is also known as an equiangular quadrilateral. The quadrilateral is a closed 4-sided shape.
  • Since a rectangle contains parallel sides, it is also known as a right-angled parallelogram.
  • The parallelogram would be a quadrilateral with equal and parallel opposite sides. Rectangles are a type of parallelogram.

Now, according to the question,

Let 'P' be the perimeter of the rectangle.

Perimeter = 2(Length + Breadth)

P = 2(L + B)

The perimeter is 26 meters.

26 = 2(L + B)

L + B = 13

B = 13 - L

Now, the area of the rectangle is given as;

Area = Length×Breadth

A = L×B

Substitute the value of B in area.

A = L×(13 - L)

Area in terms of length x, Put L =x

A(x) = x(13 - x)

Therefore, the area A(x) of the rectangle in terms of the length x of one of its sides. A(x) = x(13 - x).

To know more about the rectangle, here

brainly.com/question/25292087

#SPJ4

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This is a doozy so pay attention. First thing you have to recognize is that is a trig identity, the sum identity for cosine to be exact. That formula is

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cos\alpha =\frac{3}{5} for that first angle. Now moving on to the second angle. The cosine of beta is side adjacent, 5, over the hypotenuse, 13, and we are missing the side opposite the reference angle beta. Using Pythagorean's theorem again to find the side opposite, we have that that side measures 12. Now we can find the sine of beta using that opposite side, 12, over the hypotenuse, 13. What we have now is

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When you do that you get

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