Question

the length of a rectangular playground is thrice its breadth if the perimeter of the playground is 56 metre find its dimensional​

Answer 1

$\textsf{\underline{\underline{Answer :-}}}$

The Length is 21 m and Breadth is 7 m

$\textsf{\underline{\underline{Explanation :-}}}$

Given :

Length of the Rectangle = Thrice of the Breadth

Perimeter of Rectangle = 56 m

To find :

The Length and Breadth of the Rectangle

Solution :

Consider the Breadth of the Rectangle as x

Consider the Length as 3x

$\star$ As we know :-

$\boxed{\sf{Perimeter = 2(Breadth+ Length)}}$

$\sf{\implies}2(x + 3x)= 56$

$\sf{\implies}2x + 6x = 56$

$\sf{\implies}8x = 56$

$\sf{\implies}x = \dfrac{56}{8}$

$\sf{\implies}x = 7$

Breadth = 7 m

Value of 3x

$\sf{\implies}$ 3 × 7

$\sf{\implies}$ 21

Length = 21 m

$\therefore$ The Length is 21 m and Breadth is 7 m

$\textsf{\underline{\underline{Verification :-}}}$

$\sf{\implies}2(7 + 21) = 56$

$\sf{\implies}14 + 42 = 56$

$\sf{\implies}56 = 56$

$\therefore$ The Length is 21 m and Breadth is 7 m

Answer 2

$\sf{\underline{\underline{Given:}}}$

Length of the playground = 3 (Breadth)

Perimeter of the playground = 56 m

Playground (shape) $\implies$ Rectangular


$\sf{\underline{\underline{Now:}}}$

Let the breadth of the rectangle be x.

Let the length of the rectangle be 3x.


$\sf{Formula\:for\:Perimeter\:of\:rectangle:}$

$\boxed{Perimeter = 2(Length + Breadth)}$


$\sf{\underline{\underline{Here:}}}$

$\sf{Perimeter}$ = 56 m

$\sf{Length}$ = 3x

$\sf{Breadth}$ = x

Substituting these values in the above formula we get,

$\sf{Perimeter = 2(Length + Breadth)}$

$\sf{56= 2(3x + x)}$

$\sf{56 = 6x + 2x}$

$\sf{56 = 8x}$

$\sf{ \frac{56}{8} = x}$

$\sf{7 = x}$

$\sf{\underline{\underline {Therefore:}}}$ $\boxed{x = 7}$

Now, we know that, the breadth of the playground is 7 m.


$\sf{\underline{\underline{We\:have:}}}$

$\sf{Length = 3x}$

Substituting the value of x, we get,

$\sf{Length = 3x}$

$\sf{Length = 3 \times 7}$

$\sf{Length=}$ $\boxed{ 21 \: m}$


$\sf{\underline{\underline{Therefore:}}}$

The length of the playground is 21 m and breadth is 7 m.