Answer
Verified
446.4k+ views
Hint: First, we will assume a variable for the breadth and the length will be 14 plus the breadth then we will apply the formula for perimeter of a rectangle that is: $2\left( length+breadth\right)$, after that we will substitute the value of the breadth, the length in terms of breadth and the value of perimeter from the question and hence, we will get the value of breadth. Finally we will add 14 to the breadth and get the length of the rectangle.
Complete step by step answer:
Let the breadth of the rectangle be $b$ cm.
Now it is given that the length of the rectangle is 14 cm more than the breadth therefore:
$l=b+14$ cm.
Now, it is given in the question that the perimeter of the rectangle is 448 cm.
Now we know that the perimeter of a rectangle is sum of all the sides that is:
$2\left( length+breadth\right)$
Now, we will put all the values in the formula given above, therefore we will have:
$\Rightarrow P=2\left( l+b \right)\Rightarrow 448=2\left( 14+b+b \right)\Rightarrow 448=2\left( 14+2b \right)$
Now we will take 2 on the left hand side then we will have:
$\Rightarrow \dfrac{448}{2}=\left( 14+2b \right)\Rightarrow 224=\left( 14+2b \right)$
Again we will take 14 from the right hand side to the left hand side:
$\Rightarrow 224-14=2b\Rightarrow 210=2b$
Now we will take 2 on the left hand side then we will have:
\[\Rightarrow \dfrac{210}{2}=b\Rightarrow 105=b\]
Therefore, the value of breadth is 105 cm and the length will be $l=b+14=105+14=119$ cm.
Thus, the dimension of the rectangle will be $b=105\text{ cm and }l=119\text{ cm}$.
Note: In these types of questions it is not necessary that you draw diagrams but it is anyway better. You can also do this question by taking length as $l$ and the breadth as $l-14$ , in this way you will then get:
$\begin{align}
& \Rightarrow P=2\left( l+b \right)\Rightarrow 448=2\left( l+l-14 \right)\Rightarrow 448=2\left( 2l-14 \right) \\
& \Rightarrow l=119\text{ cm} \\
\end{align}$
And the breadth will be $l-14=119-14=105\text{ cm}$.
Complete step by step answer:
Let the breadth of the rectangle be $b$ cm.
Now it is given that the length of the rectangle is 14 cm more than the breadth therefore:
$l=b+14$ cm.
Now, it is given in the question that the perimeter of the rectangle is 448 cm.
Now we know that the perimeter of a rectangle is sum of all the sides that is:
$2\left( length+breadth\right)$
Now, we will put all the values in the formula given above, therefore we will have:
$\Rightarrow P=2\left( l+b \right)\Rightarrow 448=2\left( 14+b+b \right)\Rightarrow 448=2\left( 14+2b \right)$
Now we will take 2 on the left hand side then we will have:
$\Rightarrow \dfrac{448}{2}=\left( 14+2b \right)\Rightarrow 224=\left( 14+2b \right)$
Again we will take 14 from the right hand side to the left hand side:
$\Rightarrow 224-14=2b\Rightarrow 210=2b$
Now we will take 2 on the left hand side then we will have:
\[\Rightarrow \dfrac{210}{2}=b\Rightarrow 105=b\]
Therefore, the value of breadth is 105 cm and the length will be $l=b+14=105+14=119$ cm.
Thus, the dimension of the rectangle will be $b=105\text{ cm and }l=119\text{ cm}$.
Note: In these types of questions it is not necessary that you draw diagrams but it is anyway better. You can also do this question by taking length as $l$ and the breadth as $l-14$ , in this way you will then get:
$\begin{align}
& \Rightarrow P=2\left( l+b \right)\Rightarrow 448=2\left( l+l-14 \right)\Rightarrow 448=2\left( 2l-14 \right) \\
& \Rightarrow l=119\text{ cm} \\
\end{align}$
And the breadth will be $l-14=119-14=105\text{ cm}$.
Recently Updated Pages
what is the correct chronological order of the following class 10 social science CBSE
Which of the following was not the actual cause for class 10 social science CBSE
Which of the following statements is not correct A class 10 social science CBSE
Which of the following leaders was not present in the class 10 social science CBSE
Garampani Sanctuary is located at A Diphu Assam B Gangtok class 10 social science CBSE
Which one of the following places is not covered by class 10 social science CBSE
Trending doubts
Which are the Top 10 Largest Countries of the World?
What percentage of the solar systems mass is found class 8 physics CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english 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
Give 10 examples for herbs , shrubs , climbers , creepers
Difference Between Plant Cell and Animal Cell
Why is there a time difference of about 5 hours between class 10 social science CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE