Question

The ratio of the length and breadth of a rectangular field is 3:1 . It's area is 3/4 m square. What is the perimeter of the field.

Answer 1

Answer:

Breadth = 1/2 or 0.5 m

Length = 3/2 or 1.5 m

Step-by-step explanation:

$\text{Given ratio of length to breadth = 3:1}\\\\\text{Let the length be 3x m.} \\\\\text{And, the breadth be x m.}\\\\\text{Area of rectangle = Length \times Breadth}\\\\= 3x \times x\\\\= 3x^2 \: m^2\\\\\text{But, given area = \dfrac{3}{4} \: m^2 }\\\\\\\text{According to the question,}\\\\3x^2 = \dfrac{3}{4}\\\\\\\implies x^2 = \dfrac{3}{4 \times 3} = \dfrac{1}{4}\\\\\\\implies x = \sqrt{\dfrac{1}{4}}\\\\\\= \boxed{\dfrac{1}{2}}$

$\therefore \text{Breadth = x = \dfrac{1}{2} \: m }\\\\\text{And, Length = 3 \times x = 3 \times \dfrac{1}{2} = \dfrac{3}{2} \: m }$

Hope it helps.