Question

The area of a rectangular floor is 2028 cm2

. If the length and breadth

are in the ratio of 4 : 3. Find its perimeter.​

Answer 1

• Given

• Area of rectangular floor = 2028 cm²
• Ratio of length and breadth = 4 : 3

• To find

• Perimeter

• Procedure

• We are given the ratio of length and breadth of a rectangle. Firstly, we will let the the length and breadth be 4x and 3x respectively and then substitute the values in the formula of area of rectangle.
• From there we will find the value of x and will find length and breadth and put its value in the formula of perimeter.

Formulae to be used -

• Area of rectangle = length × breadth
• Perimeter = 2(l + b)

• Solution

Let the length and breadth be 4x and 3x respectively.

Area of rectangle = Length × Breadth

Substituting the given values,

⇒ 2028 = 4x × 3x

⇒ 2028 = 12x²

⇒ 2028/12 = x²

⇒ 169 = x²

⇒ x = √169

⇒ x = 13

• The value of x is 13.

• Length of rectangle = 4x = 4 × 13 = 52 cm
• Breadth of rectangle = 3x = 3 × 13 = 39 cm

Perimeter = 2(l + b)

Substituting the given values,

⇒ 2(52 + 39)

⇒ 2(91)

⇒ 182 cm

• Perimeter = 182 cm