Question

A square in a rectangle have the same perimeter. The length of a side of the square is 4x-1. The length of the rectangle is 2x+2 and the width is 2x

Answer 1

The value x is 1, if the perimeter of square and rectangle are same. The perimeter of square and rectangle is 12 units.

Explanation:

The given is,

A square in a rectangle have the same perimeter

The length of a side of the square is 4x-1

The length of the rectangle is 2x+2 and width is 2x

Step:1

Let, a - Side of square

l - Length of the rectangle

w - Width of the rectangle

Step:2

Formula for perimeter of square is,

`p=4a`.............................(1)

Formula for perimeter of rectangle is,

`p=2(l+w)`....................(2)

Step:3

From given,

Equation (1) = Equation (2)

`4a = 2 (l+w)`

where,

a = 4x-1

l = 2x+2

w = 2x

Substitute the values,

4 ( 4x-1 ) = 2 ( 2x+2+2x )

16x - 4 = 2 (4x + 2)

16x - 4 = 8x + 4

16x - 8x = 8

8x = 8

x = 1

Step:4

Substitute the values of x,

a = 4(1)-1 = 3

l = 2(1)+2) = 4

w = 2(1) = 2

Perimeter of square and rectangle is 12 units

Result:

The value x is 1, if the perimeter of square and rectangle are same. The perimeter of square and rectangle is 12 units.