What is the width of the border of the yellow roses?

Question

you just planted a rectangular flower garden of red roses. You want to plant a border of yellow roses around the flower bed. Because you bought the same number of red and yellow roses, the areas of the border and flower bed will be equal.

Answer 1

I'm assuming the border width is the some all around.

Area of yellow = (8+x)(12+x) - 8x12

Since area of yellow = area of red: (8+x)(12+x) - 96 = 96
96 + 20x + x^2 = 192

x^2 + 20x - 96 = 0

You can now used the quadratic equations x = (-b +/-sqrt(b^2 - 4ac))/2a =(-20 +/-sqrt(400 - 4(1)(-96)))/2

(-20+28)/2 = 4

The other root is negative and so doesn't make any sense to this problem.