Question

which of the following forms a right angle Triangle:
a).12,8,13
b).8,7,12
c).8,15,17
d).5,4,9

Answer 1

answer is c

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Answer 2

From given points  a)12, 8, 13 and c) 8, 15, 17 will make a right angled triangle

Given:

a).12,8,13  b).8,7,12  c).8,15,17  d).5,4,9

To find:

Check whether given sides can make a right angled triangle

Solution:

From Pythagorean theorem,

If a, b and c are the sides of a right angled triangle where a > b > c then  

                                      a² = b²+ c²

Here, a is hypotenuse, b and c are sides

We will use this formula to check whether given sides can make a right angled triangle

a) 12, 8, 13

Here 13 > 12 > 8

⇒ 12² + 8² = 144 + 64 = 169 = 13²

⇒  12² + 8² = 13²

12,8,13 will form a right angled triangle

b) 8, 7, 12

Here, 12 > 8 > 7

⇒ 8²+ 7² = 64 +49 = 113 $\neq$ 12²  

8, 7, 12 will not make right angled triangle

c) 8, 15, 17

Here, 17 > 15 > 8

⇒ 15² + 8² = 225 + 64 = 289 = 17²

⇒ 15² + 8² = 17²  

8, 15, 17 will make a right angled triangle

d) 5, 4, 9

Here, 9 > 5 > 4

⇒ 5² + 4² = 25 + 16 = 41 $\neq$ 9²

5, 4, 9 will not make right angled triangle

From given points  a)12, 8, 13 and c) 8, 15, 17 will make a right angled triangle

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