Question

The ratio of triangle length and breadth 2:3 area is 216 cm then find the perimeter of rectangle​

Answer 1

Solution :-

Given : Ratio of Length to breadth = 2 : 3

Area of rectangle = 216 cm

Let the length and breadth of the rectangle be 2x and 3x respectively.

According to the question,

=> Area of rectangle = (Length × Breadth)

=> 2x × 3x = 216

=> 6x² = 216

=> x² = 216/6

=> x² = 36

=> x = √36 = 6

So, Length and Breadth are 2x = 2 × 6 = 12 cm and 3x = 3 × 6 = 18 cm

We know that,

Perimeter of rectangle = 2(Length + Breadth)

= 2(12 + 18)

= 2 × 30

= 60

Hence,

Perimeter of rectangle = 60 cm

Answer 2

Solution :-

Let the length of the rectangle be 2x and the breadth be 3x respectively.

Here, Area = 216 cm.

We know that,

Area of rectangle =
$length \times breadth$

Therefore,

$216 = 2x \times 3x \\ \\ 216 = 6 {x}^{2} \\ \\ {x}^{2} = \frac{216}{6} \\ \\ {x}^{2} = 36 \\ \\ x = 6$

So, length =2x
$= 2 \times 6 \\ =12$

and breadth =3x
$= 3 \times 6 \\ = 18$


Now,
Perimeter of the Rectangle
$= 2(length + breadth) \\ = 2 \times (12 + 18) \\ = 2 \times 30 \\ = 60$

Hence, the perimeter of the rectangle =60 cm.

Thanks!!