Question

$\boxed{ \huge \red \star\large \green\star \small \orange\star {\sf {Question}} \small \orange \star \large \green \star \huge \red\star}$
If the side of the chess board is smaller than it's perimeter by 42cm,find the area of the chess board.
​

Answer 1

$\huge{ \red{ \mathfrak{ Solution}}}$

$14 \: as \: because \: 14 \times 3 = 56 \: which \: is \: 42 \: greater \: than \: 14 \: .$

Answer 2

Answer:

Given :-

• The side of the chessboard is smaller than it's perimeter by 42 cm.

To Find :-

• What is the area of the chessboard.

Formula Used :-

$\clubsuit$ Perimeter Of Square Formula :

$\bigstar \: \: \sf\boxed{\bold{\pink{Perimeter_{(Square)} =\: 4 \times Side}}}\: \: \: \bigstar$

$\clubsuit$ Area Of Square Formula :

$\bigstar \: \: \sf\boxed{\bold{\pink{Area_{(Square)} =\: Side \times Side}}}\: \: \: \bigstar$

Solution :-

Let,

$\mapsto \bf Side_{(Chessboard)} =\: x\: cm$

Then, perimeter of a chessboard will be :

$\small \implies \bf Perimeter_{(Chessboard)} =\: 4 \times Side$

$\implies \sf Perimeter_{(Chessboard)} =\: 4 \times x\: cm$

$\implies \sf\bold{\green{Perimeter_{(Chessboard)} =\: 4x\: cm}}$

According to the question :

$\bigstar$ The side of the chessboard is smaller than it's perimeter by 42 cm.

So,

$\small \implies \bf Perimeter_{(Chessboard)} - Side_{(Chessboard)} =\: 42$

$\implies \sf 4x - x =\: 42$

$\implies \sf 3x =\: 42$

$\implies \sf x =\: \dfrac{\cancel{42}}{\cancel{3}}$

$\implies \sf x =\: \dfrac{14}{1}$

$\implies \sf\bold{\orange{x =\: 14}}$

Hence, the side of a chessboard is :

$\dashrightarrow \sf Side_{(Chessboard)} =\: x\: cm$

$\dashrightarrow \sf\bold{\blue{Side_{(Chessboard)} =\: 14\: cm}}$

Now, we have to find the area of the chessboard :

Given :

• Side = 14 cm

According to the question by using the formula we get,

$\longrightarrow \bf Area_{(Chessboard)} =\: Side \times Side$

$\longrightarrow \sf Area_{(Chessboard)} =\: 14\: cm \times 14\: cm$

$\longrightarrow \sf\bold{\red{Area_{(Chessboard)} =\: 196\: cm^2}}$

$\sf\bold{\purple{\underline{\therefore\: The\: area\: of\: the\: chessboard\: is\: 196\: cm^2\: .}}}$

▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃