How wide is the border?

A rectangular lawn measures 7m by 5m. A uniform border of flowers is to be planted along two adjacent sides of the lawn, as shown in the diagram. If the flowers that have been purchased will cover an area of 6.25m^2, how wide is the border?





I was thinking to do something like: (5+x)(7+x) but it didn%26#039;t work out when calculated. I need some guidance!

How wide is the border?
two sides of the rectangle


a = 7m


b = 5m





if the border have a width of x then :


Area covered = (a)(x) + (b - x)(x)


replace a and b by their values


Area= 7x + (5 - x)x = x(12 - x) = 6.25





you have to solve the equation:





x^2 - 12 x + 6.25 = 0


determinant = (12)^2 - (4)(6.25) = 119





we have two set of solutions


x1 = [12 - sqrt(119)] / 2 = 0.546 m


x2 = [12 + sqrt(119)] / 2 = 11.454 m (to be rejected because %26gt; 7m not possible)





the solution is then :


x = 0.546 m
Reply:5x + 7x + x^2 = 6.25


x^2 + 12x - 6.25 = 0


x = (-12 + sqrt(12^2 - 4(-6.25))) / 2 = .5



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