Question

the perimeter of both square and rectangle is 48cm and difference of area of square and rectangle is 4m^2.what is the breadth of rectangle option are 10,12,14

Answer 1

Length and width are 10 cm and 14 cm

Explanation:

If the perimeter of the square is 48 cm, then its side has length

`48/ 4=12\ cm`

The area of the square is

`12* 12=144\ cm^2`

If the perimeter of the rectangle is 48 cm, then the sum of the length and the width is

`48/ 2=24\ cm`

Let

Length = x cm, then

Width = 24 - x cm and the area of the rectangle is

`x(24-x)\ cm^2`

The difference of area of square and rectangle is
`4\ cm^2,` then

`144-x(24-x)=4\\ \\144-24x+x^2=4\\ \\x^2-24x+140=0\\ \\D=(-24)^2-4\cdot 1\cdot 140=576-560=16\\ \\√(D)=4\\ \\x_(1,2)=(-(-24)\pm 4)/(2\cdot 1)=(24\pm 4)/(2)=12\pm 2=14,\ 10`

If
`x=14\ cm,` then
`24-x=24-14=10\ cm`.

If
`x=10\ cm,` then
`24-x=24-10=14\ cm`