Question

The length of a rectangle is 4 less than thrice its breadth If its perimeter is 40 cm find its dimensions.

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Answer 1

Answer:

Hope this helped you

Step-by-step explanation:

Let the breadth of a rectangle = x m.

Thrice its breadth=3x m

Length of a rectangle= 3x-6 m

Perimeter of  a rectangle = 2(l+b)

=2(3x−6+x)

=2(4x−6)

=8x−12

But we are given perimeter=148 m

8x−12=148

8x=148+12

8x=160

x=20 metres

Breadth=x= 20 metres

and Length=3x−6=3×20−6=60−6=54 metres.

Answer 2

Given :

• The length of a rectangle is 4 less than thrice its breadth and its perimeter is 40 cm.

$\rule{200pt}{3pt}$

To Find :

• Find the dimensions of rectangle .

$\rule{200pt}{3pt}$

Solution :

✧ Formula Used :

$\large{\color{red}{\bigstar}} \: \: {\underline{\boxed{\green{\sf{ Perimeter{\small_{(Rectangle)}} = 2(Length + Breadth)}}}}}$

$\qquad{\rule{150pt}{1pt}}$

✧ According to Question :

• ➺ let breadth of Rectangle be y .Hence,

${\orange{:\longmapsto{\sf{ Breadth \: of \: Rectangle \: = y }}}}$

• ➺ Length of the Rectangle is 4 less than thrice its Breadth .Hence,

${\orange{:\longmapsto{\sf{ Length \: of \: Rectangle \: = 3y - 4 }}}}$

$\qquad{\rule{150pt}{1pt}}$

✧ Calculating the Value of y :

${\dashrightarrow{\qquad{\sf{ Perimeter = 2(Length + Breadth)}}}} \\ \\ \ {\dashrightarrow{\qquad{\sf{ 40 = 2[(3y - 4 ) + y ] }}}} \\ \\ \ {\dashrightarrow{\qquad{\sf{ 40 = [(6y - 8) + 2y ]}}}} \\ \\ \ {\dashrightarrow{\qquad{\sf{ 40 = 8y - 8 }}}} \\ \\ \ {\dashrightarrow{\qquad{\sf{ 40 + 8 = 8y }}}} \\ \\ \ {\dashrightarrow{\qquad{\sf{ 48 = 8y }}}} \\ \\ \ {\dashrightarrow{\qquad{\sf{ \cancel\dfrac{48}{8} = y }}}} \\ \\ \ {\qquad \: \: \: {\pink{:\longmapsto{\underline{\overline{\boxed{\purple{\sf{6}}}}}}}}}{\gray{\bigstar}}$

$\qquad{\rule{150pt}{1pt}}$

✧ Calculating the Dimensions :

$\large{\blue{\longmapsto{\underline{\underline{\red{\sf{ Length = 3y - 4 = 3 \times 6 - 4 = 14 \: cm}}}}}}}$

$\\ \large{\blue{\longmapsto{\underline{\underline{\red{\sf{ Breadth = y = 6 \: cm}}}}}}}$

$\qquad{\rule{150pt}{1pt}}$

✧ Therefore :

❝ Length of the Rectangle is 14 cm and its breadth is 6 cm . ❞

$\\ {\underline{\rule{300pt}{9pt}}}$