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

Question

Ratling [72]

1 year 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] · Answer 1 · 2024-08-05T23:31:50+03:00

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.