Question

find the area of a rectangle when lenght is x+4 and breadth is x-2 and perimeter is 56​

Answer 1

$\red{\bigstar}\underline{\underline{\textsf{\textbf{ Given }}}}\begin{cases} & \sf{Length\:of\;a\:rectangle = \bf{(x + 4)\:units}} \\ & \sf{Breadth\:of\:a\:rectangle = \bf{(x - 2)\:units}} \\ & \sf{Perimeter\;of\;a\:rectangle = \bf{56\;units}} \end{cases}$

$\red{\bigstar}\underline{\underline{\textsf{\textbf{ To\:Find\::- }}}}$

• $\sf{Area\:of\:a\:rectangle\:=\:\bf{?}}$

$\red{\bigstar}\underline{\underline{\textsf{\textbf{ Answer\::- }}}}$

• $\sf{Area\:of\:a\:\:rectangle\:=\:\bf{187\:sq.units}}$

$\red{\bigstar}\underline{\underline{\textsf{\textbf{ Step\:by\:step\:explanation\::- }}}}$

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• Using formula of perimeter of rectangle to find value of x.

$\qquad\red\bigstar\:{\tiny{\underline{\boxed{\bf{\green{Perimeter_{(Rectangle)} = 2(Length + Breadth)}}}}}}$

$\red{\bigstar}\underline{\underline{\textsf{\textbf{ Putting\:all\:known\:values\::-}}}}$

$\dashrightarrow\qquad\sf 56 = 2[(x + 4) + (x - 2)]$

$\dashrightarrow\qquad\sf 56 = 2(x + 4 + x - 2)$

$\dashrightarrow\qquad\sf 56 = 2(x + x + 4 - 2)$

$\dashrightarrow\qquad\sf 56 = 2(2x + 2)$

$\dashrightarrow\qquad\sf 56 = 4x + 4$

$\dashrightarrow\qquad\sf 56 - 4 = 4x$

$\dashrightarrow\qquad\sf 52 = 4x$

$\dashrightarrow\qquad\sf \dfrac{52}{4} = x$

$\dashrightarrow\qquad\sf \dfrac{\cancel{52}}{\cancel{4}} = x$

$\dashrightarrow\qquad{\boxed{\frak{\pink{x = 13}}}}\:\purple\bigstar$

$\red{\bigstar}\underline{\underline{\textsf{\textbf{ Hence, }}}}$

• Length of a rectangle = x + 4 = 13 + 4 = 17 units.
• Breadth of a rectangle = x - 2 = 13 - 2 = 11 units.

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• Using formula of area of rectangle to find it's area.

$\qquad\red\bigstar\:{\tiny{\underline{\boxed{\bf{\green{Area_{(Rectangle)} = Length\:\times\:Breadth}}}}}}$

$\red{\bigstar}\underline{\underline{\textsf{\textbf{ Putting\:all\:known\:values\::- }}}}$

$\dashrightarrow\qquad\sf Area_{(Rectangle)} = 17 \:\times\: 11$

$\dashrightarrow\qquad{\boxed{\frak{\pink{ Area_{(Rectangle)} = 187\:sq.units}}}}\:\purple\bigstar$

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$\small\therefore\:{\underline{\sf{Hence,\:area\:of\:a\:rectangle\:is\:\bf{187\:sq.units}\:\sf{respectively.}}}}$

$\red{\bigstar}\underline{\underline{\textsf{\textbf{ Note\::- }}}}$

• Diagram is in attachment !

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Answer 2

$\pink{\dag}{\underline{\textsf{\textbf{ Given\::- }}}}$

• Length = x + 4 units

• Breadth = x - 2 units

• Perimeter of rectangle = 56 units

$\pink{\dag}{\underline{\textsf{\textbf{ To\:find\::- }}}}$

• Area of rectangle

$\pink{\dag}{\underline{\textsf{\textbf{ Solution\::- }}}}$

$\implies\sf Length\: of \:rectangle\: = x + 4 \: units$

$\implies\sf Breadth \: of rectangle \: = x - 2 \: units$

$\implies\sf Perimeter \: of \: rectangle = 56 units$

We have to find the value of x.

$\pink{\dag}{\underline{\textsf{\textbf{ Perimeter \: of \: rectangle = 2(length + breadth) }}}}$

$\implies\sf 56 = 2 (l + b)$

$\implies\sf 56 = 2 (x + 4 + x - 2)$

$\implies\sf 56 = 2 (2x + 2)$

$\implies\sf 56 = (4x + 4)$

$\implies\sf 56 - 4 = 4x$

$\implies\sf 52 = 4x$

$\implies\sf x = \dfrac{52}{4}$

$\implies\sf x =\cancel\dfrac{52}{4}$

$\implies\sf x = 13$

$\sf\green{Length\: of \:rectangle \:= x + 4 = 13 + 4 = 17\: units}$

$\sf\green{Breadth\: of\: rectangle\: = x - 2 = 13 - 2 = 11 \:units}$

$\pink{\dag}{\underline{\textsf{\textbf{ Formula :-}}}}$

$\implies\sf Area \: of \: rectangle = length \times breadth$

$\implies\sf Area \: of \: rectangle = 17units \times 11units$

$\implies\sf Area \: of \: rectangle = 187sq.units$

$\pink{\dag}{\underline{\textsf{\textbf{ Therefore,}}}}$

$\large\sf\red {Area\: of \:rectangle\: = 187sq.units}$