Question

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)

Answer 1

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

What is rectangle?

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

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