Question

If the length of the sides of a square are rational numbers, which of the following is true?

a) Half of its side length is always an integer.
b) Length of its diagonal is an irrational number.
c) Its area is definitely a perfect square number.
d) Its perimeter may or may not be a rational number.​

Answer 1

Answer:

c and d are correct

Step-by-step explanation:

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Answer 2

Given,

The length of sides of a square is rational numbers.

To Find,

The true option among the given.

Solution,

To check which option is correct we need to check each option with examples.

For the first one, Given, "Half of its side length is always an integer".It is obviously not possible. Because if we suppose a rational number be $\frac{1}{2}$ , half of this will be a rational too.

For the 2nd option, the Length of its diagonal is an irrational number.

That's true , because,  Length of its diagonal is always an irrational number,

As we know diagonal = $\sqrt{2}$ × Length of one side.

For option C, the area may not be a perfect square number. Because if the side length is $\frac{1}{2}$ then the area will be $(\frac{1}{2} )^{2} =\frac{1}{4}$ , which is a rational.

For option, d we know perimeter = 4×one side. So obviously it will be rational.

Hence, the correct option is (b) the length of its diagonal is an irrational number.