2. Which of the following can be the sides of a right triangle?
a) 2cm, 2cm, 5cm c) 10cm, 6cm, 9cm
b) 17cm, 15cm, 8cm d) 12cm, 13cm, 15cm
Answers
ANSWER:
HYPOTENUSE = 17 cm
OTHER TWO SIDES = 15cm, 8cm
GIVEN:
a) 2 cm, 2 cm, 5 cm
b) 17 cm, 15 cm, 8 cm
c) 10 cm, 6 cm, 9 cm
d) 12 cm, 13 cm, 15 cm
TO FIND:
The length of vertices of a right angled triangle.
THEOREM USED:
PYTHAGORAS THEOREM:
The square of hypotenuse is equal to the sum of the squares of the other two sides.
(Hypotenuse)² = A² + B² [ where A and B be the length of other two sides. ]
EXPLANATION:
Hypotenuse is the longest side of a right angled triangle.
a) Longest side = 5 cm
A = 2 cm
B = 2 cm
(5)² = 25
2² + 2² = 4 + 4 = 8
25 ≠ 8
Hence it does not form a right angled triangle.
b) Longest side = 17 cm
A = 15 cm
B = 8 cm
17² = 289
15² + 8² = 225 + 64 = 289
289 = 289
Hence it forms a right angled triangle.
c) Longest side = 10 cm
A = 6 cm
B = 9 cm
10² = 100
9² + 6² = 81 + 36 = 116
100 ≠ 116
Hence it does not form a right angled triangle.
d) Longest side = 15 cm
A = 12 cm
B = 13 cm
15² = 225
12² + 13² = 144 + 169 = 313
225 ≠ 313
Hence it does not form a right angled triangle.