Question

The area of a playing card is 60 square centimeters. The perimeter is 32 centimeters. What are the dimensions of the playing card?

Answer 1

we’re looking for values of xy=60 (area) and 2x+2y = 32 (perimeter).

So we rearrange the 2nd equation to 2y = 32-2x.
Then y = 16-x. Put this equation into the first one to get x(16-x) =60, then expand to get 16x - x^2 -60 = 0.

Then put this into the quadratic equation to get x1= 6 and x2=10. Then plug these values into y = 16-x.
10=16-6, 6=16-10.
So the y values are 10 and 6.
As they come in pairs, x1=6, y1=10. And x1=10, y1=6.

As playing cards are usually taller than they are wide, the dimensions are in 10cm (height) x 6cm (width)