Question

Explain why a square with an area of 20 cm2 does not have a whole-number side length

Answer 1

Step-by-step explanation:

We have,

Area = 20 cm²

Let me try to explain it to you in a general fashion using equations, then I will give you a clear image verbally.

Now,

Let the side of the square be 's'.

Then,

Area of the square with side 's' = side × side

Area = s × s

Area = s²

Then, according to the Question,

Area = s² = 20 cm²

Then,

s² = 20 cm²

Thus, we can find the length of side by taking square root on both sides.

So,

√s² = √20

s = √(2 × 2 × 5)

s = √(2² × 5)

s = 2√5 cm

Thus, we can say that Side length of a square is the square root of it's Area.

Thus, to understand a simple explanation to the Question verbally, we must understand the situation,

Then, explanation would be,

Since, the side length of a square is the square root of it's Area, only numbers that are perfect squares will give a whole number side lengths and all the other numbers that aren't a perfect square will never give a whole number side length.

To be precise, Squares of Area like 1, 4, 9, 16, 25, 36 and so on will only have a whole number side lengths, all the other squares that have a non perfect square number as it's Area will always have a non whole number side length.

So, your main explanation would be,

Squares that have perfect squares as it's Area will always have a whole number side lengths while all the other squares that have a non perfect square number as it's Area will always have a non whole number side length.

It is due to the simply fact that their prime factorization will always have at least one prime number with a power of 1.

Hope it helped you and believing you understood it...All the best

Answer 2

Given: area of the square$=20cm^{2}$.

To explain: the side of the given square is not a whole number.

Solution:

Find the side of the square.

Area of the square$=(side)^{2}$

$\[\begin{array}{l} \Rightarrow 20 = {\left( {side} \right)^2}\\ \Rightarrow side = \sqrt {20} cm\\ \Rightarrow side = 2\sqrt 5 cm\end{array}\]$

Observe that. the side of square is calculated to be $2\sqrt{5}$ cm which is not a whole number.

Therefore, the side of the square can never be a whole number if its area is $20cm^{2}$.