Question

The perimeter of a rectangle is 54 cm .if the length of the rectangle is 18 cm ,find its area

Answer 1

Question:

$\text{The perimeter of a rectangle is 54 cm}$ .

$\text{If the length of the rectangle is 18 cm ,find its area.}$

Given:

$\red{\boxed{Perimeter = 54cm}}$

$\red{\boxed{Length = 18cm}}$

Taken:

$\text{Let the breadth be x cm}$

Concept:

$\red{\boxed{Perimeter = 2\big(length + Breadth\big)}}$

$\red{\boxed{Area = length × Breadth}}$

To find:

$\text{The breadth and the area of the rectangle}$

To find the Breadth:

Using the formula for perimeter of the rectangle :

$\red{\boxed{54cm = 2\big(18 + x\big)}}$

$\red{\boxed{\dfrac{54}{2}cm = \big(18 + x\big)}}$

$\red{\boxed{27cm = \big(18 + x\big)}}$

$\red{\boxed{(27 - 18)cm = x}}$

$\red{\boxed{9 cm = x}}$

$\therefore Breadth\:is\:9 cm$

To find the Area:

Using the formula for Area of rectangle:

$\red{\boxed{Area = (18 × 9) cm^{2}}}$

$\red{\boxed{Area = 162cm^{2}}}$

$\therefore Area\:is\:162 cm^{2}$

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Answer 2

$\sf{\huge{\purple{\mathfrak{\underline{\underline{Question}}}}}}$

• The perimeter of a rectangle is 54 cm .if the length of the rectangle is 18 cm ,find its area

$\sf{\huge{\purple{\mathfrak{\underline{\underline{Solution}}}}}}$

$\sf{\bold{\green{\underline{\underline{Given}}}}}$

• Perimeter = 54cm
• length = 18cm

$\sf{\bold{\blue{\underline{\underline{To\:Find}}}}}$

• Area of the rectangle = ??

$\sf{\bold{\orange{\underline{\underline{solution}}}}}$

$\sf{\bold{\red{\boxed{perimeter = 2( l + b) }}}}$

$\sf\implies 54 = 2( 18 + b)$

$\sf\implies \dfrac{\cancel{54}}{\cancel{2}} = 18 + b$

$\sf\implies 27 = 18 + b$

$\sf \implies b = 27 - 18$

$\sf\implies b = 9cm$

$\sf{\bold{\red{\boxed{area = length \times breadth}}}}$

$\sf\implies area = 9cm \times 18cm$

$\sf\implies area = 162cm^2$

$\sf{\bold{\pink{\boxed{\dag area = 162cm^2}}}}$

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