Question

Half the perimeter of a rectangular garden, whose length is 4m more than its width
is 36m. The area of the garden is ……..


Note:- dont solve here give direct answer

Answer 1

Answer:

320 m² is the area of the garden.

Step-by-step explanation:

Given :-

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

To find :-

The area of the garden is ?

Solution :-

Let the width of the garden be x m.

Then the length of the garden will be x + 4 m.

Half the perimeter = 36

Perimeter = 36 × 2 = 72 m

ATP :-

2(Length + Breadth) = 72 m

2(x + 4 + x) = 72

2x + 2x + 8= 72

4x = 64

x = 16

Dimensions are :-

Length (x + 4) = 20 m

Breadth/Width (x) = 16 m

Area of the garden :-

Length × Breadth

20 × 16

∴ 320 m² is the area of the garden.

Answer 2

Given:

• The half perimeter of a rectangular garden is 36m
• The length of the garden is 4m more than its width

To Find:

• The area of the rectangular garden

Solution:

Here as we have given the semi perimeter of the rectangle so, let's double it to find the perimeter of the rectangle, In further let's assign suitable variables to the dimensions and find their measure out and later find it's area

Now,

→ Perimeter = 36m × 2

→ Perimeter = 72m

✰Let us assume that,

• Length of the rectangle be x + 4
• Breadth of the rectangle be x

${\underline{\frak{\dag \; As \; we \; know \; that}}}$

${\rightarrow}\qquad \qquad \bigg[ \bf Perimeter _{(rectangle)} = 2(L + B ) \bigg]$

${\underline{\bf{ \bigstar \; According \; to \; the \; question :}}}$

$:\implies \sf Perimeter = 2(L + B )\\ \\ \\ :\implies \sf 72m = 2( x + 4 + x)\\ \\ \\ :\implies \sf 72m = 2(2x + 4)\\ \\ \\ :\implies \sf 72m = 4x + 8\\ \\ \\ :\implies \sf 4x = 64\\ \\ \\ :\implies \sf x = \cancel\dfrac{64}{4}\\ \\ \\ :\implies {\pink{\underline{\boxed{\frak{x = 16 }}}\bigstar}}$

✰ Now let's find the dimensions,

• Length = x + 4 = 16 + 4 = 20cm
• Breadth = 1x = 16(1) =  16cm

✰ Now let's find the area of the rectangle,

→ Area = Length × Breadth

→ Area = 20cm × 16cm

→ Area = 320m²

Hence:

• The area of the rectangular garden is 320cm²

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