Question

A chess board contains 64 equal squares and the area of each square is $6.25c{m^2}$. A border round the board is 2 cm wide. Find the length of the side of the chess board.

Answer 1

Hint: In the given question we have to find the length of side of the chess board. For this we have to assume the length of the square board, and then find the area of 64 square boards. For this we will make an equation for the area of 64 square boards where area of one square is already given in the question. After that on equalizing both equations we will get the correct answer. We will consider only positive value.

Complete step-by-step answer:
Let side length of the square board is = x
The area of each square is chess board$ = $ $6.25c{m^2}$
Now:
The area of $64$square boards $ = {\left( {x - 4} \right)^2}$
So:
$
  {\left( {x - 4} \right)^2} = 64 \times 6.25 \\
   \Rightarrow {x^2} - 8x + 16 = 400 \\
   \Rightarrow {x^2} - 8x - 384 = 0 \\
   \Rightarrow {x^2} - 24x + 16x - 384 = 0 \\
   \Rightarrow \left( {x - 24} \right)\left( {x + 16} \right) = 0 \\
   \Rightarrow \left( {x - 24} \right) = 0 \\
  and \\
  \left( {x + 16} \right) = 0 \\
  x = 24, - 16 \\
  x = 24cm \\
 $
By ignoring the negative term value.
We get x = 24cm
This is our correct answer.

Note: First we have to assume the length of a sideboard. For these types of questions we have to remember the properties of a square, its formulas and make equations according to the given conditions. After that on equalizing both equations we will get the correct answer. i.e. x = 24cm. Remember that the area of the squad cannot be negative so we have to ignore negative terms, consider only positive value.