Question

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

Answer 1

Let Length of Rectangle be x, then Width of the Rectangle = ⅔ x

We know : Perimeter of Rectangle is 2 × (Length + Breadth)

• Substitute the value of Perimeter, Length and Breadth

⇒ 180 m = 2 × (x + ⅔ x)

⇒ 180 m = 2x + 2 × (⅔ x)

⇒ 180 m = 2x + ⁴⁄₃ x

⇒ 180 m = ⁶⁄₃ x + ⁴⁄₃ x

⇒ 180 m = ⁶⁺⁴⁄₃ x

⇒ 180 m = ¹⁰⁄₃ x

• Cross Multiply

⇒ 180 m × 3 = 10x

⇒ 540 m = 10x

• Dividing Both Sides by 10

⇒ 54 m = x

Therefore

• Length = x = 54 m
• Breadth = ⅔ x = ⁽⁵⁴ × ²⁾⁄₃ = ¹⁰⁸⁄₃ = 36 m

Answer 2

Here First We Equate 180 m to Length + Breadth multiplied 2 times where length and breadth  are assumptions of ours, Then We get value of our assumption and substitute the value into length and Breadth