Question

the ratio of the length and breadth of a rectangular field is 3:1its area is 3/4m sq. what is perimeter of the field​

Answer 1

GIVEN :-

• Ratio of Length and breadth is 3:1.
• Area of rectangular field = 3/4 m².

TO FIND :-

• The Perimeter.

SOLUTION :-

➠ Let the ratio constant be x.

➣ Length = 3x

➣ Breadth = x.

$\to \boxed{ \red{ \bf \:Area(rect.) = length \times breadth}} \\ \\ \to \rm \: \dfrac{3}{4} = x \times 3x \\ \\ \to \rm \: \dfrac{3}{4} = 3x ^{2} \\ \\ \to \rm \: \dfrac{ \cancel{3}}{4} \times \dfrac{1}{ \cancel{3}} = x ^{2} \\ \\ \to \rm \: x^{2} = \frac{1}{4} \\ \\ \to \rm \: x = \sqrt{ \dfrac{1}{4} } \\ \\ \to \boxed{ \red{ \rm \: x = \dfrac{1}{2} }}$

➠ Length = 3x = 3 × 1/2 = 3/2 m

➠ Breadth = 1/2 m.

$\to \boxed{ \red {\bf \: perimeter(rect.) = 2(l + b)}} \\ \\ \to \rm \: 2 \bigg( \dfrac{1}{2} + \dfrac{3}{2} \bigg) \\ \\ \to \rm \: 2 \bigg( \dfrac{3 + 1}{2} \bigg) \\ \\ \to \rm \: \cancel{2} \times \dfrac{4}{ \cancel{2}} \\ \\ \to \boxed{ \red{ \rm \:perimeter = 4 \: m }}$

Hence the perimeter is 4 m

VERIFICATION :-

$\to \boxed{ \red{ \bf \:Area(rect.) = length \times breadth}} \\ \\ \to \rm \: \dfrac{3}{4} = x \times 3x \\ \\ \to \rm \dfrac{3}{4} = \dfrac{1}{2} \times 3 \times \dfrac{1}{2} \\ \\ \to \rm \dfrac{3}{4} = \dfrac{1}{2} \times \dfrac{3}{2} \\ \\ \to \rm \dfrac {3}{4} = \dfrac{3}{4} \\ \\ \to \red{\rm L.H.S = R.H.S} \\ \\ \boxed{\red{\bf Hence\: \: verified}}$

Answer 2

Given ,

• The ratio of the length and breadth of a rectangular field is 3 : 1

• The area of rectangular field is 3/4 m²

Let , the length and breadth of rectangle be " 3x " and " x "

We know that , the area of rectangle is given by

Area = Length × Breadth

Thus ,

3/4 = 3x × x

3 = 12(x)²

x = √(1/4)

x = 1/2

$\therefore$ The length and breadth of rectangle are 3/2 m and 1/2 m

Now , the perimeter of rectangle is given by

Perimeter = 2(L + B)

Thus ,

Perimeter = 2(3/2 + 1/2)

Perimeter = 2(4/2)

Perimeter = 4 m

$\therefore$ The perimeter of rectangular field is 4 m