Question

A rectangular field whose length is
10 times its breadth has an
area of 75690m². What is its
Perimeters​

Answer 1

$\underline{ \underline{ \Large \pmb{\mathit{ {Given:}} }} }$

• Length of the rectangular field = 10 times its breadth

• Area of the rectangular field = 75690m²

$\underline{ \underline{ \Large \pmb{\mathit{ {To \: calculate:}} }} }$

• Perimeter

$\underline{ \underline{ \Large \pmb{\mathit{ {Calculation:}} }} }$

As per the given question, we are given that the length of the the rectangular field is 10 times its breadth and area of the rectangular field is 75690 m². We have to find the perimeter of the field. In order to find the perimeter of the field, we need the dimensions of the field, so that we can substitute the values in the formula of the perimeter of the rectangle. For that, we'll form an algebraic equation and by solving that equation we'll find the breadth and length. Then, we'll substitute the values in the formula of the perimeter of the rectangle to get our answer.

⠀⠀⠀⠀⠀_____________

Let,

• Breadth = b, so the length becomes :

• Length = 10b

[ Since, length is 10 times its breadth ]

D I A G R A M

$\sf{b \:}\huge\boxed{ \begin{array}{cc} \: \: \: \: \: \: \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \end{array}} \\ \: \: \: \: \: \sf{10b}$

Now, we know that,

$\bigstar \: \boxed{\sf { Area_{(Rectangle)} = Length \times Breadth }}$

Substituting values,

$\longrightarrow \sf {75690 = 10b \times b }$

$\longrightarrow \sf {75690 = 10{b}^{2} }$

$\longrightarrow \sf { \cancel {\dfrac{75690}{10} } = {b}^{2} }$

$\longrightarrow \sf { 7569= {b}^{2} }$

$\longrightarrow \sf { \sqrt{7569}= b }$

$\longrightarrow \sf { 87= b }$

$\longrightarrow \boxed{\pmb{ \rm { 87 \: m= Breadth }} }$ ★

Therefore, breadth is 87 m.Also,

$\longrightarrow \sf { 10b=Length }$

$\longrightarrow \sf { 10 \times 87 = Length }$

$\longrightarrow \boxed{\pmb{ \rm { 870 \: m= Length }} }$ ★

Now, calculating perimeter.

$\bigstar \: \boxed{\sf { Perimeter_{(Rectangle)} =2( Length + Breadth) }}$

$\longrightarrow \sf { Perimeter_{(Rectangle)} =2( 870 + 87) }$

$\longrightarrow \sf { Perimeter_{(Rectangle)} =2( 957) }$

$\longrightarrow \boxed{\pmb{ \rm \red{ Perimeter_{(Rectangle)} = 1914 \: m }} }$

Therefore, perimeter of the rectangular field is 1914 m.