Question

Half the perimeter of a rectangular garden, whose length is 4 m more than its width, is
36 m. Find the dimensions of the garden​

Answer 1

Answer:

Dimensions of the garden are 16 m and 20 m.

Step-by-step explanation:

As per the provided information in the given question, we have :

• Half of the perimeter of a rectangular garden = 36 m
• Length of the rectangular park = 4 m more than its width

We are asked to find the dimensions of the rectangular garden.

Clarification :

In order to find the dimensions, we'll form linear equations and then by solving that equations, we will find the dimensions. We'll be using transposition method.

★ Transposition method :

• This is the method used to solve a linear equation having variables and constants.

• In this method, we transpose the values from R.H.S to L.H.S and vice-versa and changes its sign while transposing to find the value of the unknown value.

Explication of steps :

★ According to the question,

$\longrightarrow \sf{\dfrac {Perimeter_{(Garden)}}{2} = 36 \; m}$

$\longrightarrow \sf{\dfrac {2(Length + Width)}{2} = 36 \; m}$

• Since,half of the perimeter of a rectangular garden is 36 m.

Let it be the equation (1).

Also,

$\longrightarrow \sf{ Length = 4 + Width}$

• Since, length is 4 m more than its width.

Let it be the equation (2).

Now, substitute the value of length in the equation (1) from the equation (2).

$\longrightarrow \sf{\dfrac {Perimeter_{(Garden)}}{2} = 36 \; m}$

$\longrightarrow \sf{\dfrac {2(Length + Width)}{2} = 36 \; m}$

Denoting length as 'l' and width as 'w'.

$\longrightarrow \sf{\dfrac {2(l + w)}{2} = 36}$

$\longrightarrow \sf{\dfrac {\cancel{2}(4 + w + w)}{\cancel{2}} = 36}$

$\longrightarrow \sf{4 + 2w = 36 }$

$\longrightarrow \sf{ 2w = 36 - 4 }$

$\longrightarrow \sf{ 2w = 32 }$

$\longrightarrow \sf{ w = \cancel { \dfrac{32}{2} } }$

$\longrightarrow\underline{\boxed{ \sf{ Width = 16 \; m }}} \; \bigstar$

We got that the width of the garden is 16 m. Substitute the value of width in the equation (2) to find the length of the garden.

$\longrightarrow \sf{ Length = 4 + Width}$

$\longrightarrow \sf{ Length =( 4 + 16) \; m}$

$\longrightarrow\underline{\boxed{ \sf{ Length = 20 \; m }}} \; \bigstar$

$\therefore$ Dimensions of the garden are 16 m and 20 m.