Question

the area of a rectangular field whose length is twice its breadth is 2430 m square find the perimeter of the field​

Answer 1

Answer :

• Perimeter of field is 210m

Given :

• the area of a rectangular field whose length is twice its breadth is 2430 m square

To find :

• Perimeter of the field

Solution :

Given :

• Area of rectangular field is 2430 m

then,

• Let the breadth be x
• Let the length be 2x

As we know that ,

• Area of rectangle = length × breadth

↝ 2430 = 2x × x

↝ 2430 = 2x²

↝ x² = 2430/2

↝ x² = 1225

↝ x = √1225

↝ x = 35

Then ,

• breadth = x = 35m
• length = 2x = 2(35) = 70m

Now we have to find the perimeter of field

As we know that

• perimeter of rectangle = 2(l + b)

↝ perimeter of rectangle = 2(length + breadth)

↝ 2(70 + 35)m

↝ 2(105)m

↝ 210 m

Hence Perimeter of field is 210m

Answer 2

Step-by-step explanation:

★ Concept :-

Here we use the concept of Perimeter of Rectangle. As we see, that we are given the area of the rectangular field and the length which is twice to its breadth. Then firstly, we will find out the length and breadth of the field. After that, by applying the required values in the formula of Perimeter of Rectangle we will get the answer.

Let's do it !!!

___________________

★ Formula Used :-

$\star\;\underline{\boxed{\sf{\pink{Area\ of\ Rectangle\ =\ \bf length \times breadth.}}}}$

$\star\;\underline{\boxed{\sf{\pink{Perimeter\ of\ Rectangle\ =\ \bf 2(length\ +\ breadth).}}}}$

___________________

★ Solution :-

Given,

↬ Area of the rectangular field = 2430m.

↬ Length of the field is twice to its breadth.

• Let the breadth of the rectangular field be x and the length be 2x.

------------------------------------------------------------

~ For the length and breadth of the rectangular field ::

We know that,

$\sf \mapsto {Area\ of\ Rectangular\ field\ =\ \bf length \times breadth}$

⦾ By applying the values, we get :-

$\sf \mapsto {Area\ of\ Rectangular\ field\ =\ \bf length \times breadth}$

$\sf \mapsto {2430\ =\ \bf 2x \times x}$

$\sf \mapsto {2430\ =\ \bf 2x^2}$

$\sf \mapsto {x^2\ =\ \bf \cancel \dfrac{2430}{2}}$

$\sf \mapsto {x^2\ =\ \bf 1225}$

$\sf \mapsto {x\ =\ \bf \sqrt{1225}}$

$\bf \mapsto {x\ =\ {\red {35.}}}$

~ Therefore :-

↬ Breadth = x = 35m.

↬ Length = 2x = 2 × 35 = 70m.

------------------------------------------------------------

~ For the perimeter of the rectangular field ::

We know that,

$\sf \rightarrow {Perimeter\ of\ Rectangular\ field\ =\ \bf 2(length\ +\ breadth)}$

⦾ By applying the values, we get :-

$\sf \rightarrow {Perimeter\ of\ Rectangular\ field\ =\ \bf 2(length\ +\ breadth)}$

$\sf \rightarrow {Perimeter\ of\ Rectangular\ field\ =\ \bf 2(70\ +\ 35)}$

$\sf \rightarrow {Perimeter\ of\ Rectangular\ field\ =\ \bf 2(105)}$

$\sf \rightarrow {Perimeter\ of\ Rectangular\ field\ =\ \bf 2 \times 105}$

$\bf \rightarrow {Perimeter\ of\ Rectangular\ field\ =\ \bf {\orange {210m.}}}$

∴ Hence, the perimeter of the rectangular field = 210m.

___________________

★ More to know :-

➼ The opposite sides are parallel and equal to each other.

➼ Each interior angle is equal to 90°.

➼ The sum of all the interior angles is equal to 360°.

➼ The diagonals bisect each other.

➼ Both the diagonals have the same length.

➼ Diagonal of the rectangle = √l² + b².