Question

length of a side of a square whose area is 80*244/729 square meters​

Answer 1

Answer:

$\rm \dfrac{242}{27} \; m$

Step-by-step explanation:

As per the provided information in the given question, we have :

• Area of the square is $\rm 80\dfrac{244}{729}$ m².

We are asked to calculate the length of its side.

Let the length of its side be $\ell$ .

As we know that,

$\longmapsto \bf { Area_{(Square)} = (Side)^{2} }$

So, according to the question, we can write it as,

$\longmapsto \rm { 80\dfrac{244}{729} \; m^2 = (\ell)^{2} }$

Converting the mixed fraction into proper fraction.

$\longmapsto \rm {\dfrac{58564}{729} \; m^2 = (\ell)^{2} }$

Now, putting the sign of square root (or radical) on both side to balance the equation.

$\longmapsto \rm { \sqrt{\dfrac{58564}{729} \; m^2} = \sqrt{\ell^{2}} }$

As we know that,

• √(a²) = a
• √a/√b = √(a/b)

So,

$\longmapsto \rm { \dfrac{\sqrt{58564}}{\sqrt{729}} \; m = \ell}$

___________________________

★ Finding the square root of 58564 :

By prime factorisation,

⇒ 58564 = 2 × 2 × 11 × 11 × 11 × 11

• Making the pairs of common factors and picking up each factor from each pair.

⇒ √58565 = 2 × 11 × 11

⇒ √58565 = 242

★ Finding the square root of 729 :

By prime factorisation,

⇒ 729 = 3 × 3 × 3 × 3 × 3 × 3

• Making the pairs of common factors and picking up each factor from each pair.

⇒ √729 = 3 × 3 × 3

⇒ √729 = 27

___________________________

$\longmapsto \bf { \dfrac{242}{27} \; m = \ell}$

∴ Length of the side of square is $\rm \dfrac{242}{27} \; m$ .

Answer 2

Given :-

$\sf \bullet \; Area\;of\;a\;square\;is\;\; 80 \dfrac{244}{729} \; m^{2}$

To Find :-

• Length of the side of that square.

Solution :-

❍ To calculate the length of the side of that square we must know that ::

• Area of a square = Side × Side

• Side of square = √Area

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Finding the side :-

$\sf : \; \implies Side = \sqrt{ 80 \dfrac{244}{729}}$

$\sf : \; \implies Side = \sqrt{ \dfrac{80 \times 729 + 244}{729}}$

$\sf : \; \implies Side = \sqrt{ \dfrac{58564}{729}}$

$\sf : \; \implies Side = \sqrt{ \dfrac{2 \times 2 \times 11 \times 11 \times 11 \times 11}{3 \times 3 \times 3 \times 3 \times 3 \times 3 }}$

$\sf : \; \implies Side = \dfrac{2 \times 11 \times 11}{ 3 \times 3 \times 3 }$

$\sf : \; \implies Side = \dfrac{242}{27}$

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• Henceforth, Side of the square is 242/27 m