Question

4. The sides of two triangles are given below. Determine which of them is the right triangle:
(1) a= 6 cm, b = 8 cm, c = 10 cm
(ii) a = 5 cm, b= 8 cm, c= 11 cm​

Answer 1

Explanation:

Case (i) :

Given sides of the triangle :

• a = 6cm.
• b = 8cm.
• c = 10cm.

Here, we need to check whether the sides can be a right angle triangle.

We know that, a right angle has three sides where the longest side is called as hypotenuse which is the sum of the square of the two other sides i.e., base and height.

Using the pythagoras theorem :

→ h² = p² + b²

Here,

• h (hypotenuse) = 10cm.
• p (perpendicular) = 8cm.
• b (base) = 6cm.

So,

→ 10² = 8² + 6²

→ 100 = 64 + 36

→ 100 = 100

The hypotenuse is equal to the sum of the square of the other two sides.

Yes, it can form a right angle triangle.

Case (ii) :

Using the pythagoras theorem :

• h = 11cm.
• p = 8cm.
• b = 5cm.

So,

→ 11² = 8² + 5²

→ 121 = 64 + 25

→ 121 = 89

Therefore,the hypotenuse isn't equal to the base and perpendicular

Hence, it can't form a right angled triangle.