The lengths of the sides of some triangles are given below. Which of them are right-angled?
(i) a = 15 cm, b = 20 cm c=25cm
(ii) a= 9 CM,b=12 CM and c =16cm
(iii)a=10cm,b=24cm,and c=26cm
Answers
Answer:
Both (i) & (ii)
(i) Let us assume the largest value is the hypotenuse side c=25cm
Then, by Pythagoras theorem
c2=a2+b2
252=152+202
625=225+400
625=625
The sum of square of two side of triangle is equal to the square of third side
∴ the given triangle is right-angled triangle
(ii) Let us assume the largest value is the hypotenuse side c=16cm
Then, by Pythagoras theorem
c2=a2+b2
162=92+122
256=81+144
256=225
The sum of square of two side of triangle is not equal to the square of third side
∴ the given triangle is not a right-angled triangle
(iii) Let us assume the largest value is the hypotenuse side c=26cm
Then, by Pythagoras theorem
c2=a2+b2
262=102+242
676=100+576
676=676
The sum of square of two side of triangle is equal to the square of third side
∴ the given triangle is right-angled triangle