Question

The length of sides of two triangles
are given below I Check if the
triangles are
right
angle triangles.
1)5 cm,
8 cm
11 cm
2)6 cm 8cm 10cm
​

Answer 1

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1) 6 cm, 8 cm, 10 cm

Let in ∆ABC, the longest side is AB = 10 cm

Therefore,

=> (BC)² + (AC)² = 6² + 8²

=> (BC)² + (AC)² = 6 × 6 + 8 × 8

=> (BC)² + (AC)² = 36 + 64

=> (BC)² + (AC)² = 100 = 10²

Or,

(BC)² + (AC)² = 10²

Also,

(AB)² = (10)²

In other words,

(AB)² = (BC)² + (AC)²

Therefore,

The triangle whose sides are 10 cm, 8 cm and 6 cm is a right triangle.

(2) 5 cm, 8 cm, 11 cm

Here, the longer side is 11 cm = AB

We know,

(AB)² = 11² = 121

Therefore,

(BC)² + (AC)²

=> 5² + 8²

=> 5 × 5 + 8 × 2

=> 25 + 64

Or, (BC)² + (AC)² = 89

Since,

• 89 ≠ 121

Therefore,

• The triangle with the given sides is not a right triangle.

Answer 2

Answer:

(i) We have,

                 a=6cm,b=8cm and c=10cm

Here, the larger side is c=10cm.

we have, a2+b2=62+82=36+64+100=c2

So, the triangle with the given sides is a right angle triangle.

(ii) Here, the larger side is c=11cm.

Clearly, a2+b2=25+64=89c2

So, the triangle with the given sides is not a right angle triangle.