Question

Square P has an area of 36 sq cm. If we double the side of square P , we get square Q. What will be the area of square Q? *

6 sq cm
12 sq cm
72 sq cm
144 sq cm

Answer 1

◐ Given :

• Square P has an area of 36 sq cm. If we double the side of square P , we get square Q.

◐ To find :

• What will be the area of square Q?

◐ Solution :

$\\{\large\red\dagger}\:{\sf{Area\:of\:square\:P=36cm^2}}$

• Let's find out side of square P

$\\{\Large\purple\ast}\:{\underline{\sf{\red{Area_{(square\:P)}=side\times side}}}}\:{\Large\purple\ast}$

$\implies\sf 36 = (side)^2$

$\implies\sf side=\sqrt{36}$

$\implies\sf side = 6cm$

$\therefore{\underline{\sf{Side\:of\:square\:P\:is\:\bf 6cm}}}$

__________________________

If we double the side of square P , we get square Q.

$\\\quad\large\mathfrak{\green{\underline{According\:to\:the\:given\:condition}}}$

$\\{\large\dagger}\:{\sf{Side\:of\:new\:square\:Q=6+6=12cm}}$

$\\{\Large\purple\ast}\:{\underline{\sf{\red{Area_{(square\:Q)}=side\times side}}}}\:{\Large\purple\ast}$

• Put the value of new side

$\\\implies\sf 12\times 12$

$\implies\sf 144cm^2$

$\therefore{\underline{\tt{Area\:of\:of\:square\:Q\: \bf 144cm^2}}}$

• 144 cm² is the correct option

___________________________

Answer 2

Answer:

144 cm²

Solution:

In this question, the main concept we will be using is that of the area of a square.

$\sf{Area\:of\:a\:square=a^2}$

Area of square P = 36 cm²

We know that the area of a square is a².

∴ a² = 36²

So, a = √36

a = 6 cm

It is given that when we double the side of square P, we get one side of square Q.

So, when we double the side of Square P, we have the equation:

6 x 2 = 12 cm

Hence the side of Square Q is 12 cm.

Area of a square = a²

Area of square Q = 12²

= 12 x 12

= 144 cm²

Hence the correct answer is Option D: 144 cm².

Knowledge Bytes:

→Doubling

Sometimes, we are confused when we hear to double a number. For example, if we are asked to double 8, multiply 8 with 2.

8 x 2 = 16

So, in order to double a number, simply multiply it with 2.

In the same way, to triple a number, multiply with 3 and to quadruple a number, multiply it with 4 and so on.