Question

if the length of rectangle is thrice of its breadth and it's perimeter is 32 cm then finds its area​​

Answer 1

$\large\underline{\underline{\maltese{\pmb{\sf{\red{ \: Given :-}}}}}}$

• ➬ Length of a rectangle is thrice its breadth.
• ➬ Its perimeter is 32cm.

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$\large\underline{\underline{\maltese{\pmb{\sf{\red{ \:To \: Find :-}}}}}}$

• ➬ Find the area .

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$\large\underline{\underline{\maltese{\pmb{\sf{\red{ \:Solution :-}}}}}}$

❒ First finding the dimensions :

➢ Formula Used :

$\large{\blue\bigstar{\underline{\boxed{\pink{\bf{Perimeter{\small_{(Rectangle)}} = 2(Length + Breadth)}}}}}}$

✧ Here :

• ➳ Perimeter = 32cm
• ➳ Length = 3x
• ➳ Breadth = x

➢Dimensions :

$\large{:\longmapsto{\sf{Perimeter = 2(L + B)}}}$

$\large{:\longmapsto{\sf{32 = 2(3x + x)}}}$

$\large{:\longmapsto{\sf{32 = 2 \times 4x}}}$

$\large{:\longmapsto{\sf{ \cancel\frac{32}{2} = 4x}}}$

$\large{:\longmapsto{\sf{ \cancel \frac{16}{4} = x}}}$

$\large{\red{\longrightarrow{\underline{\sf{X = 4}}}}}$

➢So :

${\green{\leadsto{\sf{Length = 3x = 3 \times 4 = 12cm}}}}$

${\green{\leadsto{\sf{Breadth = x = 4cm}}}}$

❒ Now the Area :

➢Formula Used :

$\large{\blue\bigstar{\underline{\boxed{\pink{\bf{Area{\small_{(Rectangle)}} = Length \times Breadth}}}}}}$

✧Here :

• ➳ Area = ?
• ➳ Length = 12cm
• ➳ Breadth = 4cm

➢Area :

$\large{:\longmapsto{\sf{Area = Length \times Breadth}}}$

$\large{:\longmapsto{\sf{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 12 \times 4}}}$

$\large{\red{:{\dashrightarrow{\blue{\underline{\overline{\boxed{\sf{48 \: {cm}^{2} }}}}}}}}}$

❒ Hence :

➻ Area is 48 cm² .

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Answer 2

Given :-

• Length of rectangle is thrice of its breadth.
• Perimeter of rectangle = 32 cm

To Find :-

• Area of rectangle?

Solution :-

• Let breadth of rectangle be y.
• As it is stated that length of rectangle is thrice of its breadth so length of rectangle will be 3y.

Using formula,

✪ Perimeter of rectangle = 2(l + b) ✪

Where,

• l denotes length of rectangle
• b denotes breadth of rectangle

We have,

• Length of rectangle (l) = 3y
• Breadth of rectangle (b) = y
• Perimeter of rectangle = 32 cm

Putting all values in formula,

➙ 32 = 2(3y + y)

➙ 32 = 2(4y)

➙ 32 = 2 × 4y

➙ 32 = 8y

➙ 8y = 32

➙ y = 32/8

➙ y = 4

Using formula,

✪ Area of rectangle = l × b ✪

Where,

• l denotes length of rectangle
• b denotes breadth of rectangle

We have,

• Length of rectangle (l) = 3y
• Breadth of rectangle (b) = y

Putting all values in formula,

➙ Area of rectangle = 3y × y

➙ Area of rectangle = 3 × y × y

➙ Area of rectangle = 3 × y²

Putting value of y,

➙ Area of rectangle = 3 × 4²

➙ Area of rectangle = 3 × 4 × 4

➙ Area of rectangle = 12 × 4

➙ Area of rectangle = 48 cm²

• Hence, area of rectangle is 48 cm².

Learn More :-

• Perimeter of any figure is calculated by sum of its all sides.
• Perimeter of square = 4 × side
• Area of square = (side)²
• Perimeter of equilateral ∆ = 3 × side
• Area of equilateral ∆ = √3/4 (side)²
• Perimeter of rhombus = 4 × side
• Area of rhombus = ½ × d₁ × d₂
• Perimeter of circle = 2πr
• Area of circle = πr²
• Perimeter of rectangle = 2(l + b)
• Area of rectangle = l × b

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