Question

When 4 is Subtracted from length and breadth of the rectangle, the
perimeter becomes 24; what is the mathematical form of the Statement?​

Answer 1

❍ Let the length and Breadth of the given rectangle be x and y respectively.

$\underline{\bigstar\:\boldsymbol{According\:to\; the\; Question\;:}}$⠀⠀

• It is given that, when four is subtracted from the length and Breadth of the rectangle, the perimeter becomes 24.

Therefore,

☆ Length and Breadth of the rectangle —

• Length = (x – 4)
• Breadth = (y – 4)

⠀⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━⠀⠀⠀

As we know that,

$\bigstar\;{\underline{\boxed{{\sf{\pink{Perimeter_{\;(rectangle)} = 2\Big(Length + Breadth \Big)}}}}}}$

⠀⠀⠀⠀

$\dashrightarrow\sf Perimeter_{\:(rectangle)} = 2 \bigg\{ (x - 4) + (y - 4)\bigg\} \\\\\\\dashrightarrow\sf 24 = 2\bigg\{x + y - 8\bigg\} \\\\\\\dashrightarrow\sf \dfrac{24}{2} = x + y - 8\\\\\\\dashrightarrow\sf \cancel\dfrac{24}{2} = x + y - 8\\\\\\\dashrightarrow\sf 12 = x + y - 8\\\\\\\dashrightarrow\sf 12 + 8 = x + y\\\\\\\dashrightarrow\sf \underline{\boxed{\frak{\pmb{\purple{x + y = 20}}}}}\;\bigstar$ ⠀

⠀⠀⠀⠀

$\therefore{\underline{\textsf{Hence, \;the\: required\: statement\:is\:\textbf{(x + y = 20)}.}}}$⠀

Answer 2

Answer:

Given :-

• When 4 is subtracted from length and breadth of the rectangle, the perimeter become 24.

To Find :-

• What is the mathematical form.

Formula Used :-

$\clubsuit$ Perimeter of the Rectangle :

$\longmapsto\sf\boxed{\bold{\pink{Perimeter\: of\: the\: Rectangle =\: 2(Length + Breadth)}}}$

Solution :-

Let,

$\mapsto$ Length of rectangle be x

$\mapsto$ Breadth of rectangle will be y

$\leadsto$ 4 is subtracted from the length and breadth of the rectangle :

$\mapsto$ Length of rectangle = (x - 4)

$\mapsto$ Breadth of rectangle = (y - 4)

Given :

• Perimeter = 24

According to the question by using the formula we get,

$\implies \sf 2\bigg[(x - 4) + (y - 4)\bigg] =\: 24$

$\implies \sf (x - 4 + y - 4) =\: \dfrac{\cancel{24}}{\cancel{2}}$

$\implies \sf x + y - 4 - 4 =\: 12$

$\implies \sf x + y - 8 =\: 12$

$\implies \sf x + y =\: 12 + 8$

$\implies \sf\bold{\red{x + y =\: 20}}$

$\therefore$ The mathematical form is x + y = 20 .