Question

The area of the square garden is \[4624{m^2}\]. What is its dimension ?

Answer 1

Hint: We have to find the measure of the dimensions or the measure of each side of the square garden . We will solve this question using the concept of area of a square shape . We are given the value of the area of the square , we would simplify the values and taking the root we can find the measure of the dimension of the square garden . The units of measurement of the dimensions of the garden would also be the same as that of the square root of the units of measurement of the area of the garden .

Complete step-by-step solution:
Given :
The area of the square garden is \[4624{m^2}\] .
But , we know that the formula for the area of a square shape is given as :
\[Area = side \times side\]
Now , using the above formula for the area of a square shape , we get a equation for the area of garden as :
\[Area = 4624{m^2} - (1)\]
Let \[x\] be the dimensions of the side of the square garden .
As , we know that all the sides of a square are equal is measurement .
Then , the formula becomes as :
\[Area = x \times x--\left( 2 \right)\]
Comparing equations \[\left( 1 \right)\] and \[\left( 2 \right)\] , we get
\[x \times x = 4624{m^2}\]
Now , taking the square root , we get the value of \[x\] as
\[x = 68{\text{ }}m\]
Hence , each of the dimensions of the square garden is equal to \[68{\text{ }}m\] .

Note: As , we can clearly see that the units of measurements of the two quantities i.e. the area and the dimensions of the square gardens were different . It is so because a measure such as the length , breadth , height of an object are \[1 - D\] \[\left( {1 - Dimensional} \right)\] quantities on the other hand the measurements such as the area , curved surface area all these are \[2 - D\] \[\left( {2 - Dimensional} \right)\] quantities . So , they have different units but relate to a single measurement I.e. metre in this question .