Question

The area of a square park is $ \left( {400 \pm 4} \right){m^2} $ . What is the length of one side of the park?
A. $ (20 \pm 2)m $
B. $ \sqrt {404} m $
C. $ (20 \pm 0.1)m $
D. $ (20 \pm \sqrt 2 )m $

Answer 1

Hint: The area of the square park is already given so using the formula of area of the square we will first find the length of one side of the park and then the length of maximum difference in the length of the square park using the tolerance formula.
Area of square = $ A = {l^2} $
Therefore, the tolerance formula is
 $ \dfrac{{\Delta A}}{A} = 2\dfrac{{\Delta l}}{l} $

Complete step-by-step answer:

First, we will find the length of one side of the square park
Area of square park = $ 400{m^2} $
Area of square = $ A = {l^2} $
 $ \therefore 400{m^2} = {l^2} $
Taking square root on both sides,
 $ \sqrt {400{m^2}} = \sqrt {{l^2}} $
 $ 20m = l $
Therefore, the length of one side of the square park is $ 20m $ .
The maximum difference in the area of square park is given as
 $ \Delta A = 4{m^2} $
We know,
 $ A = {l^2} $
Therefore,
 $ \dfrac{{\Delta A}}{A} = 2\dfrac{{\Delta l}}{l} $
Substituting the values in the formula we get,
 $ \dfrac{4}{{400}} = 2 \times \dfrac{{\Delta l}}{{20}} $
Now solving for $ \Delta l $ we get,
 $ \therefore \Delta l = \dfrac{{4 \times 20}}{{400 \times 2}} $
 $ \therefore \Delta l = \dfrac{2}{{20}} = \dfrac{1}{{10}} = 0.1m $
The maximum difference in length of one side of a square park is $ 0.1m $
So, the total length of the one side of a square park becomes $ (20 \pm 0.1)m $ .
The correct answer is option $ (C) $ . $ (20 \pm 0.1)m $ .
So, the correct answer is “Option C”.

Note: A square is a regular quadrilateral, this means that it has 4 identical sides and 4 identical angles (ninety-degree angles, or one hundred-gradian angles or proper angles). it could also be described as a rectangle in which adjoining sides have the same length. A square with vertices ABCD could be denoted $ \square ABCD $ .