Question

Perimeter of the rectangular field Is equal to perimeter ofthe square field of side 16.Scm . If the length of the rectangular field is twice the breadth, find the length and breadth of the rectangular field​

Answer 1

Length=22cm

Breadth=11cm

Step-by-step solution:

A/Q, Perimeter of the rectangular field=Perimeter of the square field

Perimeter of the square field= 4×16.5cm

=66cm

Therefore, Perimeter of the rectangular field= 66cm

Now, Let the breadth be B

A/Q, Length=2B

We know that the perimeter of a rectangle= 2(L+B)

2(L+B)=66

2(2B+B)=66

2×3B=66

6B=66

B=66/6

Therefore, B=11

Breadth of the rectangular field=11cm

Length of the rectangular field= 2×11cm

=22cm

Hope this helps!

PEACE

Answer 2

❍ Let the length and breadth of rectangular field be 2x cm and x cm respectively.

$\\ \underline{\bigstar\boldsymbol{According\;to\;the\;given\;Question:}}$

• Here,The perimeter of rectangular field is equal to perimeter of the square and the side of square is 16.5 cm.So we can use the formula of perimeter of rectangle and perimeter of square to find the length and breadth of rectangular field.

Let's do it,

$\dashrightarrow$Perimeter of rectangle = Perimeter of square

$\dashrightarrow$Perimeter of rectangle = 4 × 16.5

$\dashrightarrow$Perimeter of rectangle = 66 cm

• Therefore,The perimeter of rectangle is 66cm.

Now,Appying the values,

$\\ \twoheadrightarrow \: \sf{66 = 2(2x + x)} \\ \\ \twoheadrightarrow \: \sf{66 = 4x + 2x} \\ \\ \twoheadrightarrow \: \sf{66 = 6x} \\ \\ \twoheadrightarrow \: \sf{x = \frac{ \cancel{66}}{ \cancel{6}}} \\ \\ \twoheadrightarrow \: \underline{\boxed{\frak{x = 11}}} \red{ \bigstar}$

Hence,

• The length of rectangular field is 2 × 11 = 22 cm
• The breadth of rectangular field is 11 cm.

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$\\ \underline{\frak{\dag\;Formula\;used\;here:}} \\ \\ \red{ \bigstar} \: \underline{\boxed{\sf{Perimeter_{(rectangle)} = 2(l + b)}}}\\ \\ \green{ \bigstar} \: \underline{\boxed {\sf{Perimeter_{(square)} = 4 \times \: side}}}$

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