The area of rectangle can be represented as a function of \(r\) as \(\boxed{{\mathbf{Area = 8}}{{\mathbf{r}}^{\mathbf{2}}}}\) and the perimeter of rectangle can be represented as a function of \(r\) as \(\boxed{{\mathbf{Perimeter = 12r}}}\).
Further explanation:
The diameter of the circle is two times of the radius.
It can be mathematically expressed as,
\(\text{diameter}=2\times\text{radius}\)
Given:
Two equal circles of radius \(r\) are inscribed in a rectangle.
Step by step explanation:
Step 1:
First determine the length and breadth of the rectangle.
The length of the rectangle is two times of the diameter.
Therefore, the length of the rectangle can be found as,
\(\text{lenght}=2\times2r\)
Here, \(2r,\) is the diameter of the circle.
The breadth of the rectangle is equal to the diameter.
Therefore, the breadth of the rectangle can be found as,
\({\text{breadth}} = 2r\)
Step 2:
(a)
The formula of the area of the rectangle can be calculated as,
\({\text{area}} = l \times b\)
The area of the rectangle can be found as,
\(\begin{aligned}{\text{area}} &= l \times b\\&= 4r \times 2r\\&= 8{r^2}\\\end{aligned}\)
Therefore, the area of rectangle can be represented as a function of \(r\) as \({\text{area}} = 8{r^2}\).
Step 3:
(b)
The formula of the perimeter of the rectangle can be calculated as,
\({\text{perimeter}} = 2\left( {l + b} \right)\)
The perimeter of the rectangle can be found as,
\(\begin{aligned}{\text{perimeter}} &= 2\left( {l + b} \right)\\&= 2\left( {4r + 2r} \right)\\&= 2\left( {6r} \right)\\&= 12r\\\end{aligned}\)
Therefore, the perimeter of rectangle can be represented as a function of \(r\) as \({\text{perimeter}} = 12r\).
Learn more:
- Learn more about the function is graphed below https://brainly.com/question/9590016
- Learn more about the symmetry for a function https://brainly.com/question/1286775
- Learn more about midpoint of the segment https://brainly.com/question/3269852
Answer details:
Grade: Middle school
Subject: Mathematics
Chapter: Perimeter and area.
Keywords: Perimeter, area, rectangle, inscribed, circle, function of \(r\), formula, diameter, radius, length, breadth, two times, mathematically expressed.
