Answer
Verified
410.7k+ views
Hint:Start by mentioning all the formulas that are necessary in these types of questions. Then next start by evaluating the perimeter of the rectangle then further evaluate the area of the rectangle.The perimeter and area of the rectangle are given by $2(l + b)$ and $A = l \times b$.
Complete step by step answer:
First we will start off by mentioning the formula for the perimeter of the rectangle, which is given by $2(l + b)$ where $l$ is the length of the rectangle and $b$ is the breadth or width of the rectangle. Now, we will substitute the values of the terms in the above mentioned formula,
\[
P = 2(l + b) \\
\Rightarrow P = 2((3\sqrt 7 + 3\sqrt 5 ) + (2\sqrt 7 - 2\sqrt 5 )) \\
\Rightarrow P = 2(3\sqrt 7 + 2\sqrt 7 + 3\sqrt 5 - 2\sqrt 5 ) \\
\therefore P = 2(5\sqrt 7 + \sqrt 5 )\]
Hence, the value of the perimeter of the rectangle will be \[2(5\sqrt 7 + \sqrt 5 )\].
Now we will evaluate the area of the rectangle. Area of the rectangle is given by the formula,
$A = l \times b$ where $l$ is the length of the rectangle and $b$ is the breadth or width of the rectangle.Now, we will substitute the values of the terms in the above mentioned formula,
$
A = l \times b \\
\Rightarrow A = (3\sqrt 7 + 3\sqrt 5 ) \times (2\sqrt 7 - 2\sqrt 5 ) \\
\Rightarrow A = (3\sqrt 7 \times 2\sqrt 7 ) + (3\sqrt 7 \times - 2\sqrt 5 ) + (3\sqrt 5 \times 2\sqrt 7 ) + (3\sqrt 5 \times - 2\sqrt 5 ) \\
\Rightarrow A = 6 \times 7 - 6\sqrt {35} + 6\sqrt {35} - 6 \times 5 \\
\Rightarrow A = 42 - 30 \\
\therefore A = 12 $
Hence, the value of the area of the rectangle will be $12$ sq. units.
Therefore, the area and perimeter of the rectangle will be $12$ sq. units and \[2(5\sqrt 7 + \sqrt 5 )\] units.
Note:While substituting the terms make sure you are taking into account the correct dimensions along with their units. Check if all the given terms have the same units, if not then convert all the terms to one single unit.The perimeter of a rectangle is the total length of all the sides of the rectangle. Hence, we can evaluate the perimeter by adding all four sides of a rectangle. Since opposite sides of a rectangle are always equal we need to evaluate only two sides to calculate the perimeter of the rectangle.
Complete step by step answer:
First we will start off by mentioning the formula for the perimeter of the rectangle, which is given by $2(l + b)$ where $l$ is the length of the rectangle and $b$ is the breadth or width of the rectangle. Now, we will substitute the values of the terms in the above mentioned formula,
\[
P = 2(l + b) \\
\Rightarrow P = 2((3\sqrt 7 + 3\sqrt 5 ) + (2\sqrt 7 - 2\sqrt 5 )) \\
\Rightarrow P = 2(3\sqrt 7 + 2\sqrt 7 + 3\sqrt 5 - 2\sqrt 5 ) \\
\therefore P = 2(5\sqrt 7 + \sqrt 5 )\]
Hence, the value of the perimeter of the rectangle will be \[2(5\sqrt 7 + \sqrt 5 )\].
Now we will evaluate the area of the rectangle. Area of the rectangle is given by the formula,
$A = l \times b$ where $l$ is the length of the rectangle and $b$ is the breadth or width of the rectangle.Now, we will substitute the values of the terms in the above mentioned formula,
$
A = l \times b \\
\Rightarrow A = (3\sqrt 7 + 3\sqrt 5 ) \times (2\sqrt 7 - 2\sqrt 5 ) \\
\Rightarrow A = (3\sqrt 7 \times 2\sqrt 7 ) + (3\sqrt 7 \times - 2\sqrt 5 ) + (3\sqrt 5 \times 2\sqrt 7 ) + (3\sqrt 5 \times - 2\sqrt 5 ) \\
\Rightarrow A = 6 \times 7 - 6\sqrt {35} + 6\sqrt {35} - 6 \times 5 \\
\Rightarrow A = 42 - 30 \\
\therefore A = 12 $
Hence, the value of the area of the rectangle will be $12$ sq. units.
Therefore, the area and perimeter of the rectangle will be $12$ sq. units and \[2(5\sqrt 7 + \sqrt 5 )\] units.
Note:While substituting the terms make sure you are taking into account the correct dimensions along with their units. Check if all the given terms have the same units, if not then convert all the terms to one single unit.The perimeter of a rectangle is the total length of all the sides of the rectangle. Hence, we can evaluate the perimeter by adding all four sides of a rectangle. Since opposite sides of a rectangle are always equal we need to evaluate only two sides to calculate the perimeter of the rectangle.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Which are the Top 10 Largest Countries of the World?
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Difference Between Plant Cell and Animal Cell
Give 10 examples for herbs , shrubs , climbers , creepers
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
How do you graph the function fx 4x class 9 maths CBSE
Write a letter to the principal requesting him to grant class 10 english CBSE