Question

5. The lengths of the sides of some triangles are gien below. Find out which ones are right angled
triangles :
(i) 8, 15, 17.
(ii) 40, 20, 30.​

Answer 1

i}  8, 15, 17

8² = 64,

15²  = 225,

17²  = 289  

Now, 64 + 225 = 289  

∴ 8​​​​​​​2 + 15​​​​​​​2  = 17​​​​​​​2  

The above expression is of the from (hypotenuse)​​​​​​​2  = (base)​​​​​​​2  + (height)​​​​​​​2  

∴ The sides of lengths 8,15,17 will form a right-angled triangle.

ii} 40, 20, 30

40​​​​​​​²  = 1600,

20​​​​​​​²  = 400,

30​​​​​​​²  = 900

But, 400 + 900 ≠ 1600  

∴ 20​​​​​​​2  + 30​​​​​​​2  ≠ 40​​​​​​​2  

∴ The above expression is not of the from (hypotenuse)​​​​​​​² = (base)​​​​​​​²  + (height)​​​​​​​²

∴ The sides of lengths 40, 20, 30 will not form a right-angled triangle.