Answer
423.9k+ views
Hint: We’ll take the help of properties of the triangle to solve this question, applying those properties we’ll get some inequalities that will help us find the correct answer. Then we’ll look for the option which will best satisfy our inequalities to get the correct answer.
Complete step by step answer:
Given data: the length of two sides of the triangle is 4 cm and 7 cm.
Let the measure of third side of the triangle is ‘l’ cm
We know that the sum of two sides of a triangle is always greater than the measure of the third side.
We can say that,
$
{\text{l < 4 + 7}} \\
\Rightarrow {\text{l < 11cm}} \\
$
It is also said that the measure of a side of a triangle is always greater than the difference of the other two sides of the triangle, concluding that
$
{\text{l > }}\left| {{\text{7 - 4}}} \right| \\
\Rightarrow {\text{l > 3cm}} \\
$
From the above inequalities, we can say that ‘l’ lies between 3 cm and 11 cm.
From the options only (C)6 satisfy the above statement.
Hence, option (C) is the correct answer
Note: We can say that in a triangle always lies between the difference and the sum of the other two sides i.e., here
$
\left| {{\text{7 - 4}}} \right|{\text{ < l < 7 + 4}} \\
\Rightarrow {\text{3cm < l < 11cm}} \\
$
Therefore, (C)6 cm
Complete step by step answer:
Given data: the length of two sides of the triangle is 4 cm and 7 cm.
Let the measure of third side of the triangle is ‘l’ cm
We know that the sum of two sides of a triangle is always greater than the measure of the third side.
We can say that,
$
{\text{l < 4 + 7}} \\
\Rightarrow {\text{l < 11cm}} \\
$
It is also said that the measure of a side of a triangle is always greater than the difference of the other two sides of the triangle, concluding that
$
{\text{l > }}\left| {{\text{7 - 4}}} \right| \\
\Rightarrow {\text{l > 3cm}} \\
$
From the above inequalities, we can say that ‘l’ lies between 3 cm and 11 cm.
From the options only (C)6 satisfy the above statement.
Hence, option (C) is the correct answer
Note: We can say that in a triangle always lies between the difference and the sum of the other two sides i.e., here
$
\left| {{\text{7 - 4}}} \right|{\text{ < l < 7 + 4}} \\
\Rightarrow {\text{3cm < l < 11cm}} \\
$
Therefore, (C)6 cm
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)