Question

$\textsf{\textbf{\red{Please \: Help}}}$

✤ The width of a rectangle is two-thirds its length. If the perimeter is 180 metres, find the
dimensions of the rectangle.​ ✤

▬▭▬▭▬▭▬▭▬▭▬▭▬▭▬▭​

Answer 1

Given :

• Width of a Rectangle is two thirds its length.
• Perimeter of Rectangle is 180m.

To Find :

• Dimensions of Rectangle.

Solution :

$\longmapsto\tt{Let\:Length=x}$

As Given that Width of a Rectangle is two thirds its length. So ,

$\longmapsto\tt{Breadth=\dfrac{2}{3}x}$

Using Formula :

$\longmapsto\tt\boxed{Perimeter\:of\:Rectangle=2(l+b)}$

Putting Values :

$\longmapsto\tt{180=2\bigg(\dfrac{x}{1}+\dfrac{2}{3}x\bigg)}$

$\longmapsto\tt{180=2\bigg(\dfrac{3x+2x}{3}\bigg)}$

$\longmapsto\tt{\cancel\dfrac{180}{2}=\dfrac{5x}{3}}$

$\longmapsto\tt{90\times{3}=5x}$

$\longmapsto\tt{270=5x}$

$\longmapsto\tt{x=\cancel\dfrac{270}{5}}$

$\longmapsto\tt\bf{x=54}$

Value of x is 54...

Therefore :

$\longmapsto\tt\bf{Length=54m}$

$\longmapsto\tt{Breadth=\dfrac{2}{{\cancel{3}}}\times{{\cancel{54}}}}$

$\longmapsto\tt\bf{36m}$

Answer 2

Answer:

Solution:

It is given that width of a rectangle is two - thirds its length.

Let -

→ Length = x m.

→ Width = 2/3x

Also, it is given that perimeter of rectangle is 180 m.

→ 2(B + L) = 180

→ 2(2/3x + x) = 180

→ 2/3x + x = 180/2

→ 2/3x + x = 90

→ (2x + 3x)/3 = 90

→ 5x = 90 × 3

→ 5x = 270

→ x = 270/5

→ x = 54 m

Hence, length of rectangle is 54 m.

Now,

→ Width = 2/3x

→ Width = 2/3 × 54

→ Width = 36 m

Hence, width of rectangle is 36 m.

______________________

Answer:

Length = 54 m

Width = 36 m