Question

the ratio of length and breadth of a rectangular plot is 3 is to 2 and its area is 1200 square metre then find its perimeter​

Answer 1

Question

the ratio of length and breadth of a rectangular plot is 3 is to 2 and its area is 1200 square metre then find its perimeter

Solution

Given:-

• the ratio of length and breadth of a rectangular plot = 3:2
• Area of rectangular plot = 1200 m²

Find:-

• Perimeter of rectangular plot

Explanation

Let,

• Length of rectangular plot = 3x
• Breadth of rectangular plot = 2x

Using formula

★ Perimeter of rectangle = 2 ×(Length + Breadth )

★ Area of rectangle = Length × Breath .

So,

==> Area of rectangle = 3x × 2x

==> Area of rectangular plot = 6x²

==> 1200 = 6x²

==> x² = 1200/6

==> x = √200

==> x = 10√2

Hence

• Length of rectangular plot = 3x = 3*10√2 = 30.√2 m
• Breadth of rectangular plot = 2x = 2*10√2 = 20.√2 m

Now,

==>Perimeter of rectangular plot = 2×(30√2 + 20.√2)

==> Perimeter of rectangular plot = 2×(50.√2)

==> Perimeter of rectangular plot = 100.√2 m

Thus

• perimeter of rectangular plot = 100.√2 m

__________________

Answer 2

✬ Perimeter = 100√2 m ✬

Step-by-step explanation:

Given:

• Ratio of length and breadth of a rectangular plot is 3 : 2
• Area of rectangular plot is 1200 m².

To Find:

• What is the perimeter of rectangular plot ?

Solution: Let x be the common in given ratio. Therefore,

• Length = 3x
• Breadth = 2x

★ Area of Rectangle = (Length x Breadth) ★

But area given is 1200 m²

A/q

$\implies{\rm }$ 1200 m² = (3x) $\times$ (2x)

$\implies{\rm }$ 1200 = 6x²

$\implies{\rm }$ 1200/6 = x²

$\implies{\rm }$ 200 = x²

$\implies{\rm }$ √200 = x

$\implies{\rm }$ √2 x 2 x 2 x 5 x 5 = x

$\implies{\rm }$ 10√2 m = x

So, Length = 3x = 3(10√2)m = 30√2 m

Breadth = 2x = 2(10√2)m = 20√2 m

Now, we have to find the Perimeter of rectangular plot ➲

★Perimeter of Rectangle =2(Length x Breadth)★

$\implies{\rm }$ Perimeter = 2 (30√2 + 20√2)

$\implies{\rm }$ 2 ( 50√2 )

$\implies{\rm }$ 100√2 m

Hence, The Perimeter of rectangular plot is 100√2 m.