Answer
Verified
394.8k+ views
Hint: To solve this question, we should know the relation between the length of the side of the square and the area of the square. The area of the square of side ‘s’ meter is given by the formula ${{s}^{2}}\text{ }{{m}^{2}}$. Using this relation, we get the side of the square as $s=\sqrt{2304}\text{ }m$ If $d={{a}^{x}}{{b}^{y}}{{c}^{z}}$ then square root of d is given by $\sqrt{d}={{a}^{\dfrac{x}{2}}}{{b}^{\dfrac{y}{2}}}{{c}^{\dfrac{z}{2}}}$. To get the value of the square root of 2304, we should do the prime factorization of 2304 and divide the powers of prime numbers by 2 to get the square root of the number.
Complete step-by-step solution:
In the question, we are given the area of the square plot as 2304 ${{m}^{2}}$ and asked to find the side of the square plot. We know that the relation between the area and side of the square is
Area $A={{s}^{2}}\text{ }{{m}^{2}}\to \left( 1 \right)$.
In the question A = 2304 ${{m}^{2}}$. Substituting the value of A in equation-1 we get
$\begin{align}
& {{s}^{2}}=2304 \\
& s=\sqrt{2304} \\
\end{align}$
We should get the value of square root of 2304 to get the value of s. Using the factorisation method to get the square root of 2304, we get
$\begin{align}
& 4\left| \!{\underline {\,
2304 \,}} \right. \\
& 4\left| \!{\underline {\,
576 \,}} \right. \\
& 4\left| \!{\underline {\,
144 \,}} \right. \\
& 4\left| \!{\underline {\,
36 \,}} \right. \\
& 3\left| \!{\underline {\,
9 \,}} \right. \\
& 3\left| \!{\underline {\,
3 \,}} \right. \\
& \left| \!{\underline {\,
1 \,}} \right. \\
\end{align}$
We can write that $2304={{4}^{4}}\times {{3}^{2}}$
If $d={{a}^{x}}{{b}^{y}}{{c}^{z}}$ then square root of d is given by $\sqrt{d}={{a}^{\dfrac{x}{2}}}{{b}^{\dfrac{y}{2}}}{{c}^{\dfrac{z}{2}}}$.
Using this property as d =2304, we get
$\sqrt{2304}={{4}^{\dfrac{4}{2}}}\times {{3}^{\dfrac{2}{1}}}={{4}^{2}}\times {{3}^{1}}=16\times 3=48$
So, the length of the side s = 48 m.
$\therefore $ The side of the square plot is 48 m and answer is option-A.
Note: We can do the problem in an alternative way by observing the options and given area. The number 2304 lies between 1600 and 2500 which are the squares of 40 and 50 respectively. So, the square root of 2304 also lies between 40 and 50. The last digit of 4 in 2304 is possible if the square root has the last digit as 2 or 8. So the two options for the answer are 42 and 48. By calculating the squares of 42 and 48, we get the answer. If 2304 is not a perfect square, the factorization procedure helps in getting the closest value.
Complete step-by-step solution:
In the question, we are given the area of the square plot as 2304 ${{m}^{2}}$ and asked to find the side of the square plot. We know that the relation between the area and side of the square is
Area $A={{s}^{2}}\text{ }{{m}^{2}}\to \left( 1 \right)$.
In the question A = 2304 ${{m}^{2}}$. Substituting the value of A in equation-1 we get
$\begin{align}
& {{s}^{2}}=2304 \\
& s=\sqrt{2304} \\
\end{align}$
We should get the value of square root of 2304 to get the value of s. Using the factorisation method to get the square root of 2304, we get
$\begin{align}
& 4\left| \!{\underline {\,
2304 \,}} \right. \\
& 4\left| \!{\underline {\,
576 \,}} \right. \\
& 4\left| \!{\underline {\,
144 \,}} \right. \\
& 4\left| \!{\underline {\,
36 \,}} \right. \\
& 3\left| \!{\underline {\,
9 \,}} \right. \\
& 3\left| \!{\underline {\,
3 \,}} \right. \\
& \left| \!{\underline {\,
1 \,}} \right. \\
\end{align}$
We can write that $2304={{4}^{4}}\times {{3}^{2}}$
If $d={{a}^{x}}{{b}^{y}}{{c}^{z}}$ then square root of d is given by $\sqrt{d}={{a}^{\dfrac{x}{2}}}{{b}^{\dfrac{y}{2}}}{{c}^{\dfrac{z}{2}}}$.
Using this property as d =2304, we get
$\sqrt{2304}={{4}^{\dfrac{4}{2}}}\times {{3}^{\dfrac{2}{1}}}={{4}^{2}}\times {{3}^{1}}=16\times 3=48$
So, the length of the side s = 48 m.
$\therefore $ The side of the square plot is 48 m and answer is option-A.
Note: We can do the problem in an alternative way by observing the options and given area. The number 2304 lies between 1600 and 2500 which are the squares of 40 and 50 respectively. So, the square root of 2304 also lies between 40 and 50. The last digit of 4 in 2304 is possible if the square root has the last digit as 2 or 8. So the two options for the answer are 42 and 48. By calculating the squares of 42 and 48, we get the answer. If 2304 is not a perfect square, the factorization procedure helps in getting the closest value.
Recently Updated Pages
The branch of science which deals with nature and natural class 10 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Define absolute refractive index of a medium
Find out what do the algal bloom and redtides sign class 10 biology CBSE
Prove that the function fleft x right xn is continuous class 12 maths CBSE
Find the values of other five trigonometric functions class 10 maths CBSE
Trending doubts
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Difference Between Plant Cell and Animal Cell
Select the word that is correctly spelled a Twelveth class 10 english CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
What is the z value for a 90 95 and 99 percent confidence class 11 maths CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
What organs are located on the left side of your body class 11 biology CBSE
What is BLO What is the full form of BLO class 8 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE