Which of the following length of sides will form a right angled triangle? a) 6cm, 9cm, 15cm c) 8cm, 15cm, 17cm b) 5cm, 12cm, 17cm d) 4cm, 6cm, 20cm.
Answers
Answer:
Step-by-step explanation:
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.
HENCE b) OPTION IS CORRECT.
Answer:
(c) 8cm, 15cm, 17cm
Step-by-step explanation:
In a right angle triangle, the longest side squared is equal to the other 2 sides' square added.
a^2 + b^2 = c^2 when c is the hypotenuse ( longest side in a right angle triangle)
Here, 8cm x 8cm = 64 cm
15cm x 15cm = 225
225 + 64 = 289
17 x 17 is also = 289
Since they are equal, c is the correct answer