Question

If the side of the square is tripled how many times will its Area be compared to the area of the original square.

Answer 1

Hint: Area of a square is equal to square of its side. Hence if the length of a side of a square is a unit then the Area of that square is ${{a}^{2}}$ square units. Now first find the Area of the original square using this formula. Then to find the Area of the new square substitute the side as 3 times the original side in the formula and hence find the new area of the square. Now compare the two Areas.

Complete step-by-step answer:
Let us start with considering a square whose length of side is given by x units.

Now we know the area of a square is given by the square of its side.
Hence area of square with length of side x units is equal to ${{x}^{2}}\text{squnits}$.
Let us call this original Area as ${{A}_{1}}$
Hence we have ${{A}_{1}}={{x}^{2}}..............(1)$
Now a new square is formed such that its side is 3 times the side of Original Square.
The side of our original square was x units hence, the side of the new square will be 3 times x which is 3x.

Again area of square is given by side square hence the area of new square will be
${{(3x)}^{2}}=9{{x}^{2}}$
Let us call this new Area ${{A}_{2}}$
So we have ${{A}_{2}}=9{{x}^{2}}....................(2)$.
Now from equation (1) and equation (2) we have ${{A}_{2}}=9{{A}_{1}}$
Hence the new Area is 9 times the original Area

Note: Now notice that when the side is increased 3 times the area is increased 9 times and not 3 times because the Area varies to square of side. It is a common mistake to consider the area will also be increased by 3 times but always in such sums substitute the values in Formula to get the correct option