Question

The perimeter of a rectangle is 24. write the function that describes its area in terms of one of the sides. if one side is a, the formula will be S= ____

Answer 1

The area of the rectangle whose perimeter is 24 units and one side is of 'a' units, in terms of 'a' is given as: S = a(12-a) unit²

How to find the area of a rectangle?

Suppose that the two adjacent sides of a rectangle be of 'a' units and 'b' unit lengths.

Then, we get the area of that rectangle as:

$S = a \times b \: \rm unit^2$

For this case, we're specfied that:

• One of the side of the considered rectangle is of 'a' units length.
• The perimeter of the considered rectangle = 24 units

Let the other side (adjacent) be of 'b' units length

Then, as perimeter of a rectangle = 2(sum of lengths of one pair of adjacent sides of the rectangle)

Therefore, we get:

$24 = 2(a+b)\\\text{Dividing both the sides by 2}\\12 = a + b\\b = 12 - a$

We expressed 'b' in terms of 'a' so that we can represent the area of the considered rectangle in terms of 'a' alone.

The area of the rectangle is:

$S =a \times b = a \times (12 - a) \: \rm unit^2$

Thus, the area of the rectangle whose perimeter is 24 units and one side is of 'a' units, in terms of 'a' is given as: S = a(12-a) unit²

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