Question

Half the perimeter of a rectangular garden, whose length is 4 m more than its width, is 72 m. then the length of garden is​

Answer 1

Given: Half the perimeter of a rectangular Garden is 72 m. & the length is 4 m more than it's width.

Need to find: The Length of Garden?

⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

❍ Let's say, that the width of the rectangular garden is x meters.

Then,

The Length of Garden is 4 m more than it's width:

↠⠀ Length = (width + 4)

↠⠀ Length = (x + 4) m

Half of the Perimeter of rectangular Garden is 72 meters. Therefore:

↠⠀ Perimeter = 2 × Half Perimeter

↠⠀ Perimeter = 2 × 72

↠⠀ Perimeter = 144 m

⠀

As we know that,

★ Perimeter = 2(Length + Breadth) ★

$\twoheadrightarrow\sf\quad 2\Big\{x + 4 + x\Big\} = 144$

$\twoheadrightarrow\sf\quad 2\Big\{2x + 4\Big\} = 144$

$\twoheadrightarrow\sf\quad 4x + 8 = 144$

$\twoheadrightarrow\sf\quad 4x = 144 - 8$

$\twoheadrightarrow\sf\quad 4x = 136$

$\twoheadrightarrow\sf\quad x = \cancel\dfrac{136}{4}$

$\twoheadrightarrow\quad\underline{\boxed{\pmb{\frak{x = 34}}}}\;\bigstar$

⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

Therefore,

• Width of the Garden, x = 34 m
• Length of the Garden, (x + 4) = (34 + 4) = 38 m

⠀

❝ Hence, Length of the rectangular Garden is 38 m. ❞

Answer 2

Given :-

Half the perimeter of a rectangular garden, whose length is 4 m more than its width, is 72 m.

To Find :-

Length of garden

Solution :-

We know tha

Perimeter = 2(l + b)

Half the perimeter means,

Perimeter/2 = 2(l + b)/2

Perimeter/2 = l + b

But, it is given that the half of perimeter is 72 m

72 = l + b

Let the breadth be b

Length = b + 4

72 = b + 4 + b

72 = 2b + 4

72 - 4 = 2b

68 = 2b

68/2 = b

34 = b

Hence

Breadth = b = 34 m

Length = b + 4 = 34 + 4 = 38 m

V E R I F I C A T I O N :

Perimeter = 2 × Perimeter/2

Perimeter = 2 × 72

Perimeter = 144 m

Perimeter = 2(l + b)

144 = 2(38 + 34)

144 = 2(72)

144 = 144