Question

The width of a rectangle is two - third its length . If perimeter is 180 meters , find the dimension of rectangle

Answer 1

width = 2x

length = 3x

perimeter = 2 × ( 3x + 2x )

180 = 2 × ( 3x + 2x )

= 90 = ( 3x + 2x )

90 = 5x

x = 18 m

length = 3x = 54 m

width = 2x = 36 m

Answer 2

Length = 54 m.

Width = 36 m.

Step-by-step explanation:

Given :

The width of a rectangle - two - third its length.

The perimeter - 180 meters.

To Find :

The dimension of rectangle.

Solution :

Consider the :

The Length as - n

The width as - ⅔ x

Now,

$\implies\sf Perimeter_{(\bf Rectangle)}=2(Length+Width)\\\\\\\implies\sf 180\:m=2\bigg(x+\dfrac{2x}{3}\bigg)\\\\\\\implies\sf 90\:m=\bigg(\dfrac{3x + 2x}{3}\bigg)\\\\\\\implies\sf 90\:m= \dfrac{5x}{3} \\\\\\\implies\sf 90\:m \times \dfrac{3}{5} = x\\\\\\\implies\sf 18\:m \times 3 = x\\\\\\\implies\underline{\boxed{\bf x = 54 \:m}}$

Hence,

The Dimensions of rectangle :

Length = 54 m.

Width = 36 m.

$\bigstar\;{\underline{\underline{\bf Diagram :}}}}$

$\setlength{\unitlength}{1.5cm}\begin{picture}(8,2)\thicklines\put(7.7,3){\large{A}}\put(7.5,2){\large{ \sf{}^{2x}\!/{}_{3} }}\put(7.7,1){\large{B}}\put(9.5,0.7){\sf{\large{x}}}\put(11.1,1){\large{C}}\put(8,1){\line(1,0){3}}\put(8,1){\line(0,2){2}}\put(11,1){\line(0,3){2}}\put(8,3){\line(3,0){3}}\put(11.1,3){\large{D}}\end{picture}$