Question

a playground is in the shape of a rectangle the length of a rectangle is three times its breadth and its area is 1728sq.cms find the perimeter of the rectangle​

Answer 1

Hope it helps...............

Answer 2

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

The Perimeter is 192 cm.

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

Given :

The area of the Rectangle = 1728 sq.cm

Length of Rectangle = 3 times the Breadth

To find :

The Perimeter of Rectangle

Solution :-

Consider the Breadth as x$\textsf{}$

Consider the Length as 3x $\textsf{}$

$\star$$\textsf{As we know :}$

$\boxed{\sf{Area = Length \times Breadth}}$

$\sf{\implies}3x\times \: x= 1778$

$\sf{\implies} {3x}^{2} = 1778$

$\sf{\implies} {x}^{2} = \dfrac{1778}{3}$

$\sf{\implies} {x}^{2} = 576$

$\sf{\implies}x = \sqrt{576}$

$\begin{array}{r|l} 2 & 576 \\\cline{1-2} 2 & 288 \\\cline{1-2} 2 & 144 \\ \cline{1-2} 2 & 72 \\\cline{1-2} 2 & 36 \\\cline{1-2} 2 & 18 \\\cline{1-2} 3 & 9 \\\cline{1-2} 3 & 3 \\\cline{1-2} & 1\end{array}$

576 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3

Square root = 2 × 2 × 2 × 3

= 24

$\sf{\implies}x = 24$

Breadth = 24 cm

Value of 3x

$\sf{\implies}$ 3 × 24

$\sf{\implies}$ 72

Length = 72 cm

Breadth = 24 cm

$\textsf{\large{Perimeter of Rectangle =}}$

$\star$ $\textsf{As we know :}$

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

$\sf{\implies}2(72 + 24)$

$\sf{\implies}144 + 48$

$\sf{\implies}192$

$\therefore$ The Perimeter is 192 cm