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

Answer:

Length and width are 10 cm and 14 cm

Step-by-step explanation:

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

$48\div 4=12\ cm$

The area of the square is

$12\times 12=144\ cm^2$

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

$48\div 2=24\ cm$

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

$144-x(24-x)=4\\ \\144-24x+x^2=4\\ \\x^2-24x+140=0\\ \\D=(-24)^2-4\cdot 1\cdot 140=576-560=16\\ \\\sqrt{D}=4\\ \\x_{1,2}=\dfrac{-(-24)\pm 4}{2\cdot 1}=\dfrac{24\pm 4}{2}=12\pm 2=14,\ 10$

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

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