Question

Perimeter of rectangular park is 450m. The lenghts of the sides are in ratio 3:2 find the area of the rectangle

Answer 1

The dimensions of park = 3x and 2x
Perimeter = 2(l + b)
450m = 2(3x + 2x)
450m = 2 * 5x
450/10 = x
45m = x


Dimensions = 3x = 3 * 45 = 135m
Dimension = 2x = 2 * 45 = 90m


Now

Area = l * b
➡ 135 * 90
➡ 12150m^2

Answer 2

Given : Perimeter of rectangular park = 450m

Ratio of lengths of sides = 3 : 2

Solution :-

Let the common multiple be x

Let the length be 3x and breadth be 2x

According to the given condition

Perimeter = 2(length + breadth)

☛ 450 = 2(3x + 2x)

☛ 450 = 2 × 5x

☛ 2 × 5x = 450

☛ 10x = 450

∴ x = 45

∴ Length ☛ 3x

☛ 3 × 45

☛ $\boxed{\textsf{135\:m}}$

∴ Breadth ☛ 2x

☛ 2 × 45

☛ $\boxed{\textsf{90\:m}}$

Now, we have to find Area of the rectangular park

Area of rectangle (A) ☛ length × breadth

☛ A = 135m × 90m

∴ $\boxed{\boxed{\tt{Area\:of\:rectangular\:field\:=\:12150\:m^{2}}}}$