Question

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

Answer 1

The perimeter of rectangle is 2(l+b)

l=length

b=breadth or width

given,half of perimeter of rectangle garden is 36..i.e,

(l+b)=36------------------(1)

also given length is more than breadth by 4m

l=b+4--------------------(2)

using eq(1) &(2)

(b+4)+b=36

2b=32

b=16m

put 'b' value in eq(2)

hence l=20m

dimensuons of garden are l=20m,b=16m

Answer 2

$\textbf{\underline{\underline{Answer :-}}}$

The Length is 20 m and Breadth is 16 m.

$\textbf{\underline{\underline{Explanation :-}}}$

Given :

Length is 4m more than it's Breadth

Half of it's Perimeter = 36 m

To Find :

The dimensions of the Rectangle

Solution :

Consider the :

• Breadth as x
• Length as x + 4

★ $\boxed{\sf{Perimeter=2(Length+Breadth)}}$

As it is mentioned that half of the Perimeter is 36. The Equation :

★ $\boxed{\tt{ \dfrac{2(4 + x + x)}{2} = 36}}$

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

$\tt{\implies} \: \dfrac{8+ 2x + 2x}{2} = 36$

$\tt{\implies} \: \dfrac{8+4x}{2} = 36$

$\tt{\implies} \:8+4x = 36 \times 2$

$\tt{\implies} \:8+4x = 72$

$\tt{\implies} \:4x = 72 - 8$

$\tt{\implies} \:4x = 64$

$\tt{\implies} \:x = \dfrac{64}{4}$

$\tt{\implies} \:x = 16$

$\rule{300}{1.5}$

★ Value of x + 14

$\tt{\implies} \:16 + 4$

$\tt{\implies} \:20$

$\therefore$ The Length is 20 m and Breadth is 16 m.

$\rule{300}{1.5}$

$\textbf{\underline{\underline{Verification :-}}}$

$\tt{\implies} \: \dfrac{2(4 + 16 + 16)}{2} = 36$

$\tt{\implies} \: \dfrac{8 + 32 + 32}{2} = 36$

$\tt{\implies} \: \dfrac{72}{2} = 36$

$\tt{\implies} \: 36 = 36$

$\therefore$ The Length is 20 m and Breadth is 16 m.