Question

10. The length of a rectangular plot is 144 m.
If its area is equal to area of a square with
84m side, find the Perimeter of the rect-
angle.
A) 576 m B) 386 m C) 336 m D) 193 m​

Answer 1

Given :

• Length of a Rectangular Plot = 144 m
• Area of the plot is equal to the area of square having side of 84 m

To Find :

• We have to find the Perimeter of the given Reactangular Plot

Concept Used :

☞ Area of Square is given by :

$\boxed{\sf{Area \: of \: Square = (Side)^2}}$

☞ Area of Reactangular is given by :

$\boxed{\sf{Area \: of \: Rectangle = Length \times Breadth }}$

☞ Perimeter of Rectangle is given by :

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

Solution :

Let the Breadth of Rectangle be = x

According to the Question :

Area of the Reactangular Plot is equal to the area of square of side 84 m

$\longrightarrow \boxed{\sf{Area \: of \: Reactangle = Area \: of \: square }}$

$\longrightarrow \sf{Length \times Breadth = (Side)^2}$

$\longrightarrow \sf{(x)\times 144= (84)^2}$

$\longrightarrow \sf{x = \dfrac{84 \times 84}{144}}$

$\longrightarrow \sf{x = \dfrac{7056}{144}}$

$\longrightarrow \underline{\boxed{\sf{x = 49 \: m}}}$

Breadth of the Reactangular Plot is 49 m

Perimeter of Rectangular Plot :

Perimeter can easily be determined by using the above mentioned formula

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

$\longrightarrow \sf{Perimeter = 2 \: (144 + 49)}$

$\longrightarrow \sf{Perimeter = 2 \times 193)}$

$\longrightarrow \underline{\boxed{\sf{Perimeter = 386 \: m}}}$

Hence , The Perimeter of given Reactangular Plot is 386 m

$\large {\underline{\boxed{\sf{\blue{Option \: B}}}}}\: \: \: ✔$