Which of the following could be the lengths of the sides of a 45°-45°-90° triangle?
√3/2, √3/2, √2
3√2, 3√2, 6
√3, 3, 2√3
3, 4, 5

Solution:

We have to find the lengths of the sides of a 45°-45°-90° triangle.

A 45°-45°-90° triangle is a special right triangle that has two 45 degrees angles and one 90 degrees angle. 

The side lengths are in the ratio of side 1: side 2: Hypotenuse

= n:n:n√2

= 1:1:√2

From the given option,

a. √3/2, √3/2, √2

Dividing by √3/2,

1:1:2√2/√3

Therefore, option A is not true

b. 3√2, 3√2, 6

Dividing by 3√2,

1:1:6/3√2

= 1:1:2/√2

= 1:1:√2

Therefore, option B is true.

c. √3, 3, 2√3

Dividing by√3,

= 1:1/√3:2

Therefore, option C is not true.

d. 3, 4, 5

The given real numbers cannot be reduced to 1:1:√2

Therefore, option D is not true.

Therefore, 3√2, 3√2, 6 could be the side lengths of a 45°-45°-90° triangle.

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Which of the following could be the lengths of the sides of a 45°-45°-90° triangle?

Summary:

3√2, 3√2, 6 could be the side lengths of a 45°-45°-90° triangle.