Respuesta :
The dimensions of playing card is L = 10 centimeter and W=5 centimeter, If the playing card has an area of 50 square centimeter and a perimeter of 30 centimeters.
Step-by-step explanation:
The given is,
Playing card has an area of 50 square centimeters
A perimeter of 30 centimeters
Step:1
A playing card is in the shape of rectangle,
Formula for perimeter of rectangle is,
[tex]Perimeter, P = 2(l+w)[/tex] .........................(1)
Formula for area of rectangle is,
[tex]Area, A= lw[/tex]......................................(2)
Where, l - Length of rectangle
w - Width of rectangle
Step:2
From the given values equation (1) becomes,
[tex]30 = 2(l+w)[/tex]
[tex]\frac{30}{2}=(l+w)[/tex]
[tex]15 =(l+w)[/tex]
[tex]w=15-l[/tex] .............................(3)
Width value in terms of length is calculated.
Step:2
Equation (2) becomes,
[tex]50 = (15-l)(l)[/tex]
[tex]50= 15l -l^{2}[/tex]
[tex]l^{2}-15l+50=0[/tex]
Solving the above equation,
[tex]=10[/tex]
[tex]l=10 cm[/tex]
Step:3
Equation (3) becomes,
[tex]w=15-l[/tex]
[tex]=15-10[/tex]
[tex]=5[/tex]
w = 5 cm
Result:
The dimensions of playing card is L = 10 centimeter and W = 5 centimeter, If the playing card has an area of 50 square centimeter and a perimeter of 30 centimeters.
