Question

the length and width of a rectangle are in the ratio 5:3.find the dimensions of the rectangle ,if the perimeter is 112 cm​

Answer 1

Answer:

The Length is 35 cm and Breadth is 15 cm.

Step-by-step explanation:

Given :

Ratio of Length to Breadth = 5 : 3

Perimeter of the rectangle = 112 cm

To find :

The dimensions of the rectangle

Solution :

Let the -

• Length be 5y
• Bredth be 3y

★ Perimeter = 2(Length + Breadth)

⇒ 112 = 2(5y + 3y)

⇒ 112 = 10y + 6y

⇒ 112 = 16y

⇒ y = 112/16

⇒ y = 7

$\rule{300}{1.5}$

★ Value of 5(y)

⇒ 5(7)

⇒ 35

Length = 35 cm

$\rule{300}{1.5}$

★ Value of 3y

⇒ 3(5)

⇒ 15

Breadth = 15 cm

$\therefore$ The Length is 35 cm and Breadth is 15 cm.

Answer 2

$\bold{\huge{\underline{\underline{\sf{AnsWer:}}}}}$

Length of the rectangle = 35 cm

Width of the rectangle = 15 cm

$\bold{\large{\underline{\underline{\sf{StEp\:by\:stEp\:explanation:}}}}}$

GiVeN :

• The length and width of a rectangle are in the ratio 5:3.
• Perimeter of the rectangle = 112 cm

To FiNd :

• Dimensions of the rectangle

SoLuTiOn :

Let x be the common multiple of the ratio 5:3.

•°• Length = 5x cm

Width = 3x cm

Since we have the perimeter given in the question, we can use the formula for perimeter of a rectangle.

FoRmUlA :

$\bold{\large{\boxed{\sf{\red{Perimeter\:of\:a\:rectangle\:=\:2\:(l\:+\:b)}}}}}$

Block in the values,

$\longrightarrow$ $\bold{\sf{112\:=\:2\:(5x\:+\:3x)}}$

$\longrightarrow$ $\bold{\sf{112\:=\:2\:(8x)}}$

$\longrightarrow$ $\bold{\sf{112\:=\:16x}}$

$\longrightarrow$ $\bold{\sf{\dfrac{112}{16}\:=\:x}}$

$\longrightarrow$ $\bold{\sf{7=x}}$

Substitute x = 7 in the ratio of length and width of the rectangle.

$\bold{\large{\sf{\boxed{Length\:=\:5x\:=\:5\:\times\:7\:=\:35\:cm}}}}$

$\bold{\large{\sf{\boxed{Width\:=\:3x\:=\:3\:\times\:7\:=\:15\:cm}}}}$