Question

The length and width of a rectangle atr in the ratio of 7:3. The perimeter is 80cm. Calculate the: length and width

Answer 1

Given: Ratio of length and width of the rectangle is 7: 3. & Perimeter of rectangle is 80 cm.

Need to find: The Length & Width.

⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀

❍ So, Let's consider the Length and Width of the rectangle be 7x and 3x respectively.

⠀⠀⠀

$\underline{\bf{\dag} \:\mathfrak{As\;we\;know\: that\: :}}$⠀⠀⠀⠀

$\star\:\underline{\boxed{\pmb{\sf{Perimeter = 2\bigg\lgroup Length + Breadth\bigg\rgroup}}}}$

$:\implies\sf 80 = 2\bigg\lgroup7x + 3x \bigg\rgroup$

$:\implies\sf 80 = 2 \bigg\lgroup 10x \bigg\rgroup$

$:\implies\sf 80 = 20x$

$:\implies\sf x = \cancel\dfrac{80}{20}$

$:\implies\underline{\boxed{\pmb{\frak{\purple{x = 4}}}}}\;\bigstar$

Therefore,

• Length of rectangle, 7x = 7(4) = 28 cm
• Width of rectangle is, 3x = 3(4) = 12 cm

⠀⠀⠀

$\therefore\:{\underline{\sf{Hence,\; Length\;and\; width\;of\; rectangle\;are\; {\textsf{\textbf{28 cm, 12 cm}}}\;\sf{respectively}}}}$

⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━⠀⠀

⠀⠀⠀

$\qquad\qquad\boxed{\underline{\underline{\purple{\bigstar \: \bf\:More\:Formulae\:\bigstar}}}}$

• $\sf Area\:of\:rectangle = \bf{length \times breadth}$

• $\sf Diagonal\:of\:rectangle = \bf{\sqrt{(Length)^2 + (Breadth)^2}}$

• $\sf Perimeter\:of\:square = \bf{4 \times side}$

• $\sf Diagonal\:of\:square = \bf{ \sqrt{2} \times side}$

Answer 2

Let’s consider length and breadth of rectangle be 7x and 3x

As We know that ,

Perimeter of Recatangle = 2 ( Length + Breadh )

The Perimeter of Rectangle is 80 cm

80 = 2 ( 7x + 3x )

80/2 = 7x + 3x

40 = 10x

X = 40/10

X = 4

Therefore,

Length of Rectangle is 7x = 7(4) = 28 cm

Breadth of Rectangle is 3x = 3(4) = 12cm

Length and Breadth of Rectangle are 28 cm and 12 cm , respectively