Question

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

Answer 1

$\bf\purple{QuestioN:-}$

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

$\bf\green{AnsweR:-}$

GiveN:-

Half of the perimeter of the rectangle = 36 m

Length = Breadth + 4 m

To FinD:-

The dimensions of the garden

SolutioN:-

As we know,

The formula to find the perimeter of rectangle is,

$\pink{:\implies\pmb{Perimeter~=2(l+b)}}$

Let the breadth of the rectangle be X.

Then,

Length = X + 4

Half of the perimeter is already known , and it is 36 m.

Then,

$\red{:\implies\pmb{Perimeter=2\times36=72~m}}$

That is,

$\red{:\implies\pmb{Perimeter=2\times(L+B)}}$

$\red{:\implies\pmb{72=2\times(X+X+4)}}$

$\red{:\implies\pmb{72=2\times(2X+4)}}$

$\red{:\implies\pmb{72=4X+8}}$

$\red{:\implies\pmb{72-8=4X}}$

$\red{:\implies\pmb{64=4X}}$

$\red{:\implies\pmb{X=\dfrac{64}{4}}}$

$\red{:\implies\pmb{X=16}}$

That is,

The breadth of the rectangular garden is 16 m.

Then,

Length = X + 4

            = 16 + 4 = 20 m

The dimensions of the garden ,

Length = 20 m

Breadth = 16 m

Happy Learning!!