Question

A field is rectangular is shape and it's length is 3/2 times ots breadth. If it's area is 2.4576 hectarea, what is it's perimeter

Answer 1

its breadth. If its A ... in shape and its length is 1 2.4576 hectares, what is its perimeter ? AS IT

Answer 2

Appropriate Question :-

• A field is rectangular in shape and it's length is 3/2 times it's breadth. If it's area is 2.4576 hectares, what is it's perimeter?

Answer :-

• The perimeter of the field is 6.2 hectares.

To find :-

• The perimeter of the field.

Step-by-step explanation :-

Let the breadth of the field be (x) hectares.

Then :-

• It's length will be (3/2)x, as it's length is 3/2 times it's breadth.

We know that :-

$\underline{ \boxed{ \sf Area_{(rectangle)} = Length \times Breadth}}$

Here,

• Length = (3/2)x.
• Breadth = (x).

Therefore :-

$\longrightarrow \sf{x \times \dfrac{3}{2} x = 2.4576}$

$\sf \longrightarrow x \times \dfrac{3x}{2} = 2.4576$

$\longrightarrow \sf{\dfrac{3x^2}{2} = 2.4576}$

$\longrightarrow \sf{3x^2 = 2.4576 \times 2}$

$\longrightarrow \sf{3x^2 = 4.9152}$

$\longrightarrow \sf x^2 = \dfrac{4.9152}{3}$

$\longrightarrow \sf x^2 = 1.6384$

$\sf \longrightarrow x = \sqrt{1.6384}$

$\sf \longrightarrow x = 1.28 \: hectares$

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Hence :-

$\bf Breadth = x = 1.28 \: hectares.$

$\bf Length = \dfrac{3}{2}x = \dfrac{3}{2} \times 1.28 = 1.92 \: hectares.$

Now, we know that :-

$\underline{\boxed{\sf Perimeter_{(rectangle)} = 2 \: (Length + Breadth)}}$

Therefore,

$\longrightarrow \sf{Perimeter = 2 \: (1.92 + 1.28)}$

$\longrightarrow \sf{Perimeter = 2 \: (3.2)}$

$\longrightarrow \sf{Perimeter = 6.4 \: hectares}$