Question

Two squares have sides x cm and (x+4) cm. The sum of their areas is 697$c{m^2}$. Express this as an algebraic equation in x.

Answer 1

Hint: Here we go through by applying the formula of area of square which means the square of its side. i.e.$A = {s^2}$. Here ‘s’ is the side of the square. By putting the value of sides in the formula we will find our result.

Complete step-by-step answer:
Here in the question for the first square the side of the square is given x cm.
For finding the area of first square I.e. ${A_1}$ we apply the formula of area of square.
I.e. $A = {s^2}$ now put the value of sides in this formula. We get,
${A_1} = {x^2}$
Now for the second square the side of the square is given (x+4) cm.
For finding the area of second square I.e. ${A_2}$ we apply the formula of area of square
I.e. $A = {s^2}$ now put the value of sides in this formula. We get,
${A_2} = {(x + 4)^2} = {x^2} + 8x + 16$ As we know ${(a + b)^2} = {a^2} + {b^2} + 2ab$
Now according to the question the sum of the area of the two squares is 697$c{m^2}$.
i.e. ${A_1} + {A_2} = 697c{m^2}$
$
   \Rightarrow {x^2} + {x^2} + 8x + 16 = 697c{m^2} \\
   \Rightarrow 2{x^2} + 8x + 16 = 697c{m^2} \\
 $
Hence, the required algebraic equation in x is $2{x^2} + 8x + 16 = 697c{m^2}$

Note:
Whenever we face such a type of question the key concept for solving the question is you have to remember the formula of area and also keep in mind the expansion of algebraic expression. Then by applying the condition of question you get the required result.