Answer
410.1k+ views
Hint: We are asked whether the triangle formed by the given sides form a right angled triangle. First recall the Pythagoras theorem and its condition for which a triangle can be called a right angled triangle. Check whether the sides given satisfy those conditions.
Complete step-by-step answer:
Given, the sides are \[15,17\] and \[8\]
Let the given sides be of a triangle ABC where
\[{\text{AB}} = 15\]
\[{\text{AC}} = 17\]
\[{\text{BC}} = 8\]
For a triangle to be right angled triangle, it must satisfy Pythagoras theorem which says
\[{\text{hypotenus}}{{\text{e}}^2} = {\text{bas}}{{\text{e}}^2} + {\text{perpendicula}}{{\text{r}}^2}\]
And hypotenuse is always the longest side.
Let us draw the triangle ABC
Here the longest side is \[{\text{AC}} = 17\] , so for ABC to be a right angled triangle we must have
\[{\text{A}}{{\text{C}}^2} = {\text{A}}{{\text{B}}^2} + {\text{B}}{{\text{C}}^2}\]
Let us calculate L.H.S and R.H.S separately,
L.H.S \[ = {\text{A}}{{\text{C}}^2} = {17^2} = 289\]
R.H.S \[ = {\text{A}}{{\text{B}}^2} + {\text{B}}{{\text{C}}^2}\]
\[
= {15^2} + {8^2} \\
= 225 + 64 \\
= 289
\]
We observe that L.H.S \[ = \] R.H.S
Therefore, triangle ABC or the given triangle is a right angled triangle and its hypotenuse is \[17\] .
So, the correct answer is “Option B”.
Note: Always remember the condition given by Pythagoras theorem as it is used in most of the problems. Hypotenuse is always the longest side and it is to the opposite of the right angle of the triangle. Pythagora's theorem is also used in our day to day life such as for calculating steepness of hill or mountain, height of a building, length of a ladder, used in construction and architecture works and used to find the shortest distance between two given points and also for many other purposes.
Complete step-by-step answer:
Given, the sides are \[15,17\] and \[8\]
Let the given sides be of a triangle ABC where
\[{\text{AB}} = 15\]
\[{\text{AC}} = 17\]
\[{\text{BC}} = 8\]
For a triangle to be right angled triangle, it must satisfy Pythagoras theorem which says
\[{\text{hypotenus}}{{\text{e}}^2} = {\text{bas}}{{\text{e}}^2} + {\text{perpendicula}}{{\text{r}}^2}\]
And hypotenuse is always the longest side.
Let us draw the triangle ABC
![seo images](https://www.vedantu.com/question-sets/d2cd0a45-debe-444d-8c21-6b25df1366c13578524558422796808.png)
Here the longest side is \[{\text{AC}} = 17\] , so for ABC to be a right angled triangle we must have
\[{\text{A}}{{\text{C}}^2} = {\text{A}}{{\text{B}}^2} + {\text{B}}{{\text{C}}^2}\]
Let us calculate L.H.S and R.H.S separately,
L.H.S \[ = {\text{A}}{{\text{C}}^2} = {17^2} = 289\]
R.H.S \[ = {\text{A}}{{\text{B}}^2} + {\text{B}}{{\text{C}}^2}\]
\[
= {15^2} + {8^2} \\
= 225 + 64 \\
= 289
\]
We observe that L.H.S \[ = \] R.H.S
Therefore, triangle ABC or the given triangle is a right angled triangle and its hypotenuse is \[17\] .
So, the correct answer is “Option B”.
Note: Always remember the condition given by Pythagoras theorem as it is used in most of the problems. Hypotenuse is always the longest side and it is to the opposite of the right angle of the triangle. Pythagora's theorem is also used in our day to day life such as for calculating steepness of hill or mountain, height of a building, length of a ladder, used in construction and architecture works and used to find the shortest distance between two given points and also for many other purposes.
Recently Updated Pages
Mark and label the given geoinformation on the outline class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
When people say No pun intended what does that mea class 8 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Name the states which share their boundary with Indias class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give an account of the Northern Plains of India class 9 social science 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)
Advantages and disadvantages of science
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Bimbisara was the founder of dynasty A Nanda B Haryanka class 6 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)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
10 examples of evaporation in daily life with explanations
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![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)
How do you graph the function fx 4x class 9 maths 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)