Question

14. The length and breadth of a rectangle are in
the ratio 3:2. If the area of the rectangle is
216 sq m, then find the length and breadth of
the rectangle and also find the perimeter.​

Answer 1

let length and breadth be 3x and 2x respectively

3x×2x=216

6x^2=216

x^2=36

x=6

length=18

breadth=12

2(l+b)=2(18+12)

=2(30)

=60

Answer 2

Given :-

• The length and breadth of a rectangle are in the ratio 3:2. If the area of the rectangle is 216 sq m

To find :-

• Perimeter of rectangle

Solution :-

Let the length be 3x and breadth be 2x

• Area of rectangle = 216 m²

As we know that

→ Area of rectangle = length × breadth

→ 216 = 3x*2x

→ 216 = 6x²

→ x² = 216/6

→ x² = 36

→ x = √36

→ x = 6 m

Hence,

• Length of rectangle = 3x = 18m
• Breadth of rectangle = 2x = 12cm

Perimeter of rectangle

• 2(length + breadth)

→ 2(18 + 12)

→ 2 × 30

→ 60m

Therefore ,

• Perimeter of rectangle = 60m

Verification :-

• Length = 18m
• Breadth = 12m

Area of rectangle

→ Length × breadth

→ 18 × 12

→ 216m²

Hence, verified