The area of rectangle can be represented as a function of [tex]r[/tex] as [tex]\boxed{{\mathbf{Area = 8}}{{\mathbf{r}}^{\mathbf{2}}}}[/tex] and the perimeter of rectangle can be represented as a function of [tex]r[/tex] as [tex]\boxed{{\mathbf{Perimeter = 12r}}}[/tex].
Further explanation:
The diameter of the circle is two times of the radius.
It can be mathematically expressed as,
[tex]\text{diameter}=2\times\text{radius}[/tex]
Given:
Two equal circles of radius [tex]r[/tex] 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,
[tex]\text{lenght}=2\times2r[/tex]
Here, [tex]2r,[/tex] 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,
[tex]{\text{breadth}} = 2r[/tex]
Step 2:
(a)
The formula of the area of the rectangle can be calculated as,
[tex]{\text{area}} = l \times b[/tex]
The area of the rectangle can be found as,
[tex]\begin{aligned}{\text{area}} &= l \times b\\&= 4r \times 2r\\&= 8{r^2}\\\end{aligned}[/tex]
Therefore, the area of rectangle can be represented as a function of [tex]r[/tex] as [tex]{\text{area}} = 8{r^2}[/tex].
Step 3:
(b)
The formula of the perimeter of the rectangle can be calculated as,
[tex]{\text{perimeter}} = 2\left( {l + b} \right)[/tex]
The perimeter of the rectangle can be found as,
[tex]\begin{aligned}{\text{perimeter}} &= 2\left( {l + b} \right)\\&= 2\left( {4r + 2r} \right)\\&= 2\left( {6r} \right)\\&= 12r\\\end{aligned}[/tex]
Therefore, the perimeter of rectangle can be represented as a function of [tex]r[/tex] as [tex]{\text{perimeter}} = 12r[/tex].
Learn more:
Answer details:
Grade: Middle school
Subject: Mathematics
Chapter: Perimeter and area.
Keywords: Perimeter, area, rectangle, inscribed, circle, function of [tex]r[/tex], formula, diameter, radius, length, breadth, two times, mathematically expressed.
