Question

Find the dimensions of a rectanglewhose perimeter is 28 meters and whose area is 40
square meters.​

Answer 1

Given:

☛ perimeter of rectangle = 28 m

☛ area of Rectangle = 40 m²

To Find:

☛ dimensions of the rectangle

Solution:

We know,

☛ Area of rectangle = Length × Breadth

☛ 40 = Length × Breadth

☛ Breadth = 40 / Length ...(1)

Also,

☛ Perimeter of rectangle = 2 ( Length + Breadth )

☛ 2( Length + Breadth ) = 28

☛ 2( Length + 40/ Length ) = 28 { from (1) }

☛ 2( Length² + 40 / Length ) = 28

☛ Length² + 40 / Length = 14

☛ Length² - 14 Length + 40 = 0

Let the length be x, So

☛ x² - 14x + 40 = 0

☛ x² - 10x - 4x + 40 = 0

☛ x(x - 10) - 4 (x - 10) = 0

☛ (x - 10)(x - 4) = 0

Here, we get

Length = 4 m or 10 m

Putting in (1)

☛ Breadth = 40 / Length

☛ Breadth = 40 / 4 or 40/10

☛ Breadth = 10 m or 4 m

Since, 4×4 is not satisfying the area and parameter, So we neglect it.

Therefore, Dimension of Rectangle is 10×4 or 4×10.