Question

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

Answer 1

$\purple{\underline{\sf Correct \: Question :-}}$

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

$\purple{\underline{\sf Answer :-}}$

• The length of the rectangular garden is 20 m.

• The breadth of the rectangular garden is 16 m.

$\purple{ \underline{\sf To \: find :-}}$

• The dimensions of the rectangular garden.

$\purple{\underline{\sf Solution :-}}$

• Before finding the dimensions of the rectangular garden, let's find it's perimeter.

Given :-

• Half the perimeter of the garden is 36 m.

Hence :-

• The perimeter of the garden = 36 × 2 = 72 m.

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• Now, let's find the dimensions of the garden!

Let :-

• The breadth of the garden be "x" m.

Then :-

• The length of the garden will be "x + 4" m, as it is 4 m more than it's breadth.

We know that :-

$\underline{ \boxed{\sf Perimeter \: of \: a \: rectangle = 2 \: (L + B)}}$

Where,

• L = Length.
• B = Breadth.

Here,

• Perimeter = "72" m.
• Length = "x + 4" m.
• Breadth = "x" m.

Substituting the given values in this formula,

$\implies\rm72 = 2 \: (x + 4 + x)$

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

$\rm\implies 72 = 4x + 8$

$\rm\implies 72 - 8 = 4x$

$\rm\implies 64 = 4x$

$\rm \implies \dfrac{64}{4} = x$

$\implies \overline{ \boxed{\rm16 \: m = x}}$

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Hence, the dimensions of the rectangle are as follows :-

$\bf Length = x + 4 = 16 + 4 = 20 \: m.$

$\bf Breadth = x = 16 \: m.$