Step-by-step explanation:
A playing card is in the form of a rectangle whose perimeter is equal to 28 cm and area is 45 cm².
If l and b are length and breadth of the rectangle.
Area,
[tex]A=lb[/tex]
[tex]45=lb\\\\l=\dfrac{45}{b}\ .....(1)[/tex]
Perimeter,
[tex]P=2(l+b)\\\\28=2(l+b)\\\\14=(l+b)\ ....(2)[/tex]
Put the value of l from equation (1) to equation (2). So,
[tex]14=\dfrac{45}{b}+b\\\\14=\dfrac{45+b^2}{b}\\\\14b=45+b^2\\\\b^2-14b+45=0\\\\b^2-9b-5b+45=0\\\\b(b-9)-5(b-9)=0\\\\b=5\ cm, 9\ cm[/tex]
Put the value of b in equation (1),
If b = 5 cm
[tex]l=\dfrac{45}{5}=9\ cm[/tex]
If b = 9 cm
[tex]l=\dfrac{45}{9}=5\ cm[/tex]
So, the dimensions of the playing card is 9 cm by 5 cm.
