Question

the perimeter of a rectangular cardboard is 96 cm; if its breadth is 18 cm , find the length and the area of the cardboard .

Answer 1

Perimeter = 2( l + b)
96cm = 2 ( l + 18 cm)
96cm = 2l ± 36cm
96cm - 36cm = 2l
2l = 60cm
l = 60cm/2
l = 30cm

Area = l × b = 30cm × 18cm = 540 sq. cm.


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Answer 2

$\bf{\underline{\underline \blue{Solution:-}}}$

$\sf\underline{\red{\:\:\: AnswEr:-\:\:\:}}$

• The length of the rectangular cardboard = 30 Cm
• The area of the rectangular cardboard = 540 Cm²

$\sf\underline{\red{\:\:\: Given:-\:\:\:}}$

• The Perimeter of a rectangular cardboard is 96 cm.
• The Breadth of the rectangular cardboard is 18 cm.

$\sf\underline{\red{\:\:\: Need\:To\: Find:-\:\:\:}}$

• The length of the rectangular cardboard = ?
• The area of the rectangular cardboard = ?

$\bf{\underline{\underline \blue{Explanation:-}}}$

$\dag$ In Case 1:

$\sf\underline{\green{\:\:\: Need\:To\: Find:-\:\:\:}}$

• The length of the rectangular cardboard = ?

$\sf\underline{\red{\:\:\: Formula\: Used\:Here:-\:\:\:}}$

$\bigstar \: \boxed{ \sf \: Perimeter\:of\: a\:rectangle = 2 \times (Length + Breadth) }$

$\sf\underline{\red{\:\:\: Now,Putting\:the\: values:-\:\:\:}}$

$\dashrightarrow \sf {96 = 2\times(length + 18)}$

$\dashrightarrow \sf {Length + 18 = \dfrac{\cancel{96}}{\cancel{2}} }$

$\dashrightarrow \sf {Length + 18 = 48}$

$\dashrightarrow \sf {Length = 48 - 18}$

$\dashrightarrow \sf {Length = 30}$

$\sf\underline{\pink{\:\:\: ThereFore:-\:\:\:}}$

• The length of the rectangular cardboard is 30 Cm.

$\rule{200}{2}$

$\dag$ In Case 2:

$\sf\underline{\green{\:\:\: Need\:To\: Find:-\:\:\:}}$

• The area of the rectangular cardboard = ?

$\sf\underline{\red{\:\:\:Formula\: Used\:Here:-\:\:\:}}$

$\bigstar \: \boxed{ \sf \: Area\:of\: a\:rectangle = Length \times Breadth }$

$\sf\underline{\red{\:\:\: Now,Putting\:the\: values:-\:\:\:}}$

$\dashrightarrow \sf {Area\:of\: rectangle = 30 \times 18}$

$\dashrightarrow \sf {Area\:of\: rectangle = 540}$

$\sf\underline{\green{\:\:\: ThereFore:-\:\:\:}}$

• The area of the rectangular cardboard is 540 Cm².

$\rule{200}{2}$

${\underline{\underline{\large{\sf \orange{Some\: More\: Information:-}}}}}$

• The length of the boundary of a closed figure is called the Perimeter.

$\bigstar \boxed{\green{\tt{Perimeter\:of\:a\: square = 4 \times side }}}$

$\bigstar \boxed{\green{\tt{Perimeter\:of\:a\:rectangle = 2 \times (Length + Breadth) }}}$

• The measure of the surface enclosed by a closed figure is called Area.

$\bigstar \boxed{\green{\tt{ Area\:of\: a\:square = Side \times Side }}}$

$\bigstar \boxed{\green{\tt{ Area\:of\: a\:rectangle = Length \times Breadth }}}$

$\rule{200}{2}$