Question

If c is the hypotenuse of a right triangle, of sides a, b and c, find the third side. (i) b = 12 cm and c = 13 cm (ii) a = 8 cm and b = 6 cm (iii) a = 9 cm and c = 41 cm ​

Answer 1

Step-by-step explanation:

Given that hypotenuse h=13 cm

and one side b=12 cm

Let say third side is P

Now applying pythagorus theorem:

Therefore, h

2

=b

2

+P

2

⇒13

2

=12

2

+P

2

⇒13

2

−12

2

=P

2

⇒P

2

=5

2

Thus third side of a triangle is 5 cm

Answer 2

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By Pythagoras Theorem,

hypotenuse² = perpendicular² + base²

c² = a² + b² ( or, ) c² = b² + a²

Now; by this formula, find the sides:-

(i)

=> a² = c² - b²

=> a² = 13² - 12² cm²

=> a² = 169 - 144 cm²

=> a² = 25 cm²

=> a = 5 cm

Therefore, a = 5 cm

(ii)

=> c² = a² + b²

=> c² = 8² + 6² cm²

=> c² = 64 + 36 cm²

=> c² = 100 cm²

=> c = 10 cm

Therefore, c = 10 cm

(iii)

=> b² = c² - a²

=> b² = 41² - 9² cm²

=> b² = 1,681 - 81 cm²

=> b² = 1,600 cm²

=> b = 40 cm

Therefore, b = 40 cm

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