Question

A rectangular assembly hall has a ratio of its length to its width to be 2:3. The perimeter of the hall is 30 units.
What is its area?

Answer 1

Step-by-step explanation:

2:3

let x be the multiple

2x and 3x

2x * 3x = 30

6x=30

x= 30÷6

x= 5

2x=10

3x=15

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Answer 2

Solution!!

The ratio of the length to breadth of a rectangular assembly hall is given in the question along with the perimeter of the hall. We have to find the area of the rectangular hall.

Ratio = 2:3

Perimeter = 30 units

Now, let the ratio be 2x and 3x.

Length = 2x

Breadth = 3x

We will use the perimeter formula to find the value of x.

Perimeter = 2(Length + Breadth)

30 = 2(2x + 3x)

30 ÷ 2 = 2x + 3x

15 = 5x

x = 3

2x = 2 × 3 = 6

3x = 3 × 3 = 9

Hence,

Length = 6 units

Breadth = 9 units

Now that we know the length and breadth, we can easily find the area of the hall.

Area = Length × Breadth

Area = 6 units × 9 units

Area = 54 sq. units

Hence, the area of the hall is 54 sq. units!!