Question

A triangle has sides of sqrt 2 and 3. Which could not be the length of the third side if it is a right triangle?

a. sqrt 7
b. sqrt 11
c. sqrt 13

Answer 1

Option C is correct, i.e. sqrt 13 could not be the length of the third side if it is a right triangle.

Explanation:

A triangle has sides of sqrt 2 and 3.

If it is a right triangle i.e. a² + b² = c²

There are two possible triangles:-

1. If a = √2, and b = 3. Then c² = (√2)² + 3² = 2+9 = 11 ⇒ c = √11.
2. If a = √2, and c = 3. Then b² = 3² - (√2)² = 9-2 = 7 ⇒ b = √7.

It means the third side = √7 or √11, but not √13.

Hence, option C is correct, i.e. sqrt 13 could not be the length of the third side if it is a right triangle.

Answer 2

sqrt=13 is not possible apply phythagoren theorm

a^2+b^2=c^2

(√2)^2+(3)^3=11
or other way is (3)^2- (√2)^2=7