Question

6.3 cm, 5.5 cm, and 4.2 cm
4. The breadth and perimeter of a rectangle are 8 cm and 64 cm. Find the length
of the rectangle.​

Answer 1

★ Given :

The Breadth and perimeter of a rectangle is 8 cm and 64 cm.

★ To Find :

The length of the Rectangle.

★ Solution :

Breadth = 8 cm

Perimeter = 64 cm

Perimeter Of Rectangle = 2 (L + B)

64 = 2 (L + 8)

32 = L + 8

L = 32 - 8

Length = 24 cm

Therefore,

Length of Rectangle is 24cm

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★ More To Know :

• Perimeter of Rectangle = 2 (L + B)

• Perimeter of Square = 4 × Side

• Perimeter of Traingle = a + b + c

• Perimeter of Trapezium = a+b+ c +d

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Answer 2

Answer:

$\large \underline{ \sf \pmb{Given}}$

• ➤ The breadth and perimeter of a rectangle are 8 cm and 64 cm.

$\large \underline{\sf \pmb{To \: Find} }$

• ➤ Lenght of the Rectangle

$\large \underline{\sf \pmb{Concept}}$

★ Here we know the perimeter of Rectangle is 64 cm and the Breadth of Rectangle is 8 cm..So,we need to Find the Length of Rectangle..We find the Length of Rectangle by Perimeter of Rectangle formula.

$\large\underline { \sf \pmb{Using \: Formula }}$

$\circ \underline {\boxed{\sf{Perimeter \: of \: Rectangle =2(Lenght + Breadth) }}}$

$\large \underline {\sf \pmb{Solution}}$

$\bigstar \: \underline\frak {Let \: the \: lenght \: of \: Rectangle \: be \: {\bf{x}} \: cm}$

According to the Question

${ : \implies\sf{Perimeter \: of \: Rectangle =2(Lenght + Breadth) }}$

• Substituting the values

${ : \implies\sf{64 =2(x + 8) }}$

${ : \implies\sf{64 =2x + 16 }}$

${ : \implies\sf{64 - 16 =2x }}$

${ : \implies\sf{48 =2x }}$

${ : \implies\sf{x = \cancel \dfrac{48}{2} }}$

${ : \implies\bf \red{x = 24 \: cm }}$

$\circ\underline{\boxed {\sf \purple{Lenght = 24 cm}}}$

$\large \underline{\sf \pmb{Verification}}$

${ : \implies\sf{LHS \big(2(x + 8) \big) = \big(64 \big)} RHS}$

• Substituting the values of x

${ : \implies\sf{ \big(2(24 + 8) \big) = \big(64 \big)}}$

${ : \implies\sf{ \big(2 \times 32\big) = \big(64 \big)}}$

${ : \implies\bf \red{64 \: cm=64 \: cm}}$

$\circ \underline {\boxed {\sf \purple{LHS = RHS}}}$

• $\star \: \sf\underline{Hence \: Verified} \red\checkmark$

$\large\underline{ \sf \pmb{Know \: More}}$

★ Perimeter of Rectangle

• ${ : \implies\sf \purple{Perimeter_{(Rectangle)} =2(Lenght + Breadth) }}$

★ Area of Rectangle

• ${ : \implies\sf \purple{Area_{(Rectangle)} = Lenght \times Breadth}}$

★ Diagonal of Rectangle

• ${ : \implies \sf \purple{Diagonal_{(Rectangle)}=Lenght +Breadth }}$

★ Perimeter of Square

• $: \implies \sf\purple{Perimeter_{(square)}=4 \times side }$

★ Area of Square

• $: \implies \sf \purple{Area_{(square)}= {side}^{2} }$

★ Diagonal of Square

• $: \implies \sf \purple {Diagonal_{(square)}= \sqrt{2 \times side} }$