
The perimeter of a rectangle is 13 cm and its width is $2\dfrac{3}{4}{\text{ cm}}$. Find its length.
Answer
511.8k+ views
Hint: In this question the perimeter of the rectangle is given to us and one of the sides is also known. So directly use the basic formula for the perimeter of the rectangle which is $s = 2\left( {l + b} \right)$where s is the perimeter, to obtain the unknown side.
Complete step-by-step answer:
Given data
Perimeter (s) of the rectangle $ = 13{\text{ cm}}$.
Width (b) of the rectangle $2\dfrac{3}{4}{\text{ cm}}$.
Now we have to calculate the length (l) of the rectangle.
So as we know that the perimeter of any shape is the sum of its all sides.
So from figure the perimeter of the rectangle is
$s = 2\left( {l + b} \right)$…………………… (1)
Now covert the width of the rectangle into improper fraction,
$b = 2\dfrac{3}{4} = \dfrac{{\left( {2 \times 4} \right) + 3}}{4} = \dfrac{{11}}{4}{\text{ cm}}$
Now substitute these values in equation (1) we have,
$s = 2\left( {l + b} \right)$
$ \Rightarrow 13 = 2\left( {l + \dfrac{{11}}{4}} \right)$
Divide by 2 in above equation we have,
$ \Rightarrow \dfrac{{13}}{2} = l + \dfrac{{11}}{4}$
Now simplify the above equation we have,
$ \Rightarrow l = \dfrac{{13}}{2} - \dfrac{{11}}{4} = \dfrac{{26}}{4} - \dfrac{{11}}{4} = \dfrac{{15}}{4}{\text{ cm}}$
So, the length of the rectangle is$\dfrac{{15}}{4}{\text{ cm}}$.
So, this is the required answer.
Note: Whenever we face such types of problems the key concept is simply to have the good gist of the basic perimeter formula of rectangle. This understanding of direct formula will help you get on the right track to reach the required entity.
Complete step-by-step answer:

Given data
Perimeter (s) of the rectangle $ = 13{\text{ cm}}$.
Width (b) of the rectangle $2\dfrac{3}{4}{\text{ cm}}$.
Now we have to calculate the length (l) of the rectangle.
So as we know that the perimeter of any shape is the sum of its all sides.
So from figure the perimeter of the rectangle is
$s = 2\left( {l + b} \right)$…………………… (1)
Now covert the width of the rectangle into improper fraction,
$b = 2\dfrac{3}{4} = \dfrac{{\left( {2 \times 4} \right) + 3}}{4} = \dfrac{{11}}{4}{\text{ cm}}$
Now substitute these values in equation (1) we have,
$s = 2\left( {l + b} \right)$
$ \Rightarrow 13 = 2\left( {l + \dfrac{{11}}{4}} \right)$
Divide by 2 in above equation we have,
$ \Rightarrow \dfrac{{13}}{2} = l + \dfrac{{11}}{4}$
Now simplify the above equation we have,
$ \Rightarrow l = \dfrac{{13}}{2} - \dfrac{{11}}{4} = \dfrac{{26}}{4} - \dfrac{{11}}{4} = \dfrac{{15}}{4}{\text{ cm}}$
So, the length of the rectangle is$\dfrac{{15}}{4}{\text{ cm}}$.
So, this is the required answer.
Note: Whenever we face such types of problems the key concept is simply to have the good gist of the basic perimeter formula of rectangle. This understanding of direct formula will help you get on the right track to reach the required entity.
Recently Updated Pages
What percentage of the area in India is covered by class 10 social science CBSE

The area of a 6m wide road outside a garden in all class 10 maths CBSE

What is the electric flux through a cube of side 1 class 10 physics CBSE

If one root of x2 x k 0 maybe the square of the other class 10 maths CBSE

The radius and height of a cylinder are in the ratio class 10 maths CBSE

An almirah is sold for 5400 Rs after allowing a discount class 10 maths CBSE

Trending doubts
When people say No pun intended what does that mea class 8 english CBSE

In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE

How many ounces are in 500 mL class 8 maths CBSE

Which king started the organization of the Kumbh fair class 8 social science CBSE

Advantages and disadvantages of science

What is BLO What is the full form of BLO class 8 social science CBSE
