Question

Half the perimeter of a rectangular garden, whose length is 4m more than its width, is 36 m, then the dimensions of the garden is —————-

Answer 1

Given length of rectangle is 4m more than its width and the half of its perimeter is equal to 36m.

To find the length and the width of rectangle.

Solution :

Let the width of rectangle be x m.

∴ Width of rectangle will be (4+x)m.

Now, we know that,

$\sf \boxed{\green{ \bf{ perimeter \: of \: rectangle = 2(l + b)}}}$

According To Que,

$\sf \implies \: \: \: \: \: \dfrac{2(l + b)}{2} = 36m$

$\sf \implies \: \: \: \: \: \dfrac{2(4 + x + x)}{2} = 36m$

$\sf \implies \: \: \: \: \:2(4 + 2x) = 72m$

$\sf \implies \: \: \: \: \:8 + 4x = 36m$

$\sf \implies \: \: \: \: \:4x = 36 - 8m$

$\sf \implies \: \: \: \: \:4 x= 28m$

$\sf \implies \: \: \: \: \: \boxed{\boxed{ \purple{ \bf{x = 7m}}}}$

Hence,

Width of rectangle = x = 7m

Length of rectangle = x+4 = 11m.

Answer 2

Given ,

• The length of rectangle is 4 more than its breadth

• Half of the perimeter of rectangle is 36 m

Thus ,

Perimeter of rectangle = 2 × 36 ie 72 m

Let ,

The breadth of rectangle be " x "

Then , length = " x + 4 "

We know that , the perimeter of rectangle is given by

$\boxed{ \sf{Perimeter = 2(l + b) }}$

Thus ,

72 = 2(x + 4 + x)

36 = 2x + 4

32 = 2x

x = 32/2

x = 16

Therefore ,

The length and breadth of rectangle are 20 m and 16 m