Question

the length of rectangle is four times its width . if the perimeter of rectangleis 80 m . find the length and breadth of rectangle​

Answer 1

Answer :

• Length of rectangle = 32m
• Breadth of rectangle = 8m

Given :

• The length of rectangle is four times its width
• Perimeter of rectangle is 80m

To find :

• Length of rectangle
• Breadth of rectangle

Solution :

• Let the breadth of rectangle be x

Given, the length of rectangle is four times its width so,

• Length of rectangle be 4x

Given, perimeter is 80m

We know that

• Perimeter of rectangle = 2(l + b)

Where,

• l is length of rectangle
• b is breadth of rectangle

⟹ Perimeter of rectangle = 2(l + b)

⟹ 80 = 2(4x + x)

⟹ 4x + x = 80/2

⟹ 4x + x = 40

⟹ 5x = 40

⟹ x = 40/5

⟹ x = 8 m

Finding the length and breadth of rectangle :

⟹ Length of rectangle = 4x

⟹ Length of rectangle = 4(8)

⟹ Length of rectangle = 32m

⟹ Breadth of rectangle = x

⟹ Breadth of rectangle = 8m

Hence,

• Length of rectangle = 32m
• Breadth of rectangle = 8m

Verification :

⟹ Perimeter of rectangle = 2(l + b)

⟹ 80 = 2(32 + 8)

⟹ 80 = 2(40)

⟹ 80 = 80

Hence , Verified

Answer 2

Gɪᴠᴇɴ :

• The length of rectangle is four times it's width.

• It's perimeter of rectangle is 80 m.

Tᴏ ғɪɴᴅ :

• The length and breadth of rectangle.

$\:\:\:\:\:\:\:\:\:\:\:\:\:\:━━━━━━━━━━━━━━━━━━$

$\begin{gathered}\;\;\;\;\bf{\dag}\;{\underline{\sf{ \pmb{ According \: to \: condition\ : }}}}\\\end{gathered}$

$\sf{Let \: the \: breadth \: be \: " x "}$

$\sf{ \therefore \: Length = 4x.}$

$\sf{We \: know \: that,}$

$\sf{ \underline{ \boxed{ \sf \pink{Perimeter \: of \: rectangle = 2 ( Length \: × \: breadth}}}}$

$\begin{gathered} \: \: \: \: \: \: \: \: \: \sf : \implies \: perimeter = 2(4x + x) \end{gathered}$

$\begin{gathered} \: \: \: \: \: \: \: \: \: \sf : \implies \: 80 = 2(4x + x) \\ \\\: \: \: \: \: \: \: \: \: \sf : \implies \: 80 = 2 \times 5x \\ \\ \: \: \: \: \: \: \: \: \: \sf : \implies \: 80 = 10x \\ \\ \: \: \: \: \: \: \: \: \: \sf : \implies \: x = \cancel \frac{80}{10} \\ \\ \: \: \: \: \: \: \: \: \: \sf : \implies \: \underline{ \boxed{ \sf{x = 8}}} \end{gathered}$

$\:\:\:\:\:\:\:\:\:\:\:\:\:\:━━━━━━━━━━━━━━━━━━$

$\sf{Breadth = x = 8}$

$\sf{Length = 4x = 4 \times 8 = 32}$