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 6.25 m^2, how wide is the border?

let the width of the strip x in meters
we need to find the value of x
Dimensions of the new lawn are given as
(7+x) by (5+x)
Area of the lawn is given as
6.25m^2

(7+x)(5+x) = 6.25
35 + 12x + x^2 = 6.25
x^2 + 12x+28.75 = 0
In the above equation the values are given as
a = 1, b=12, c=28.75
put these values in quadratic equation and you will get the answer.

Answer Link

boffeemadrid boffeemadrid · Answer 2 · 2022-04-03T10:42:09+02:00

The width of the border is required.

The width of the border is 0.5 m.

Area

l = Length of lawn = 7 m

w = Width of lawn = 5 m

x = Width of border

The figure of the lawn has been attached.

The area of the border will be [tex]6.25\ \text{m}^2[/tex] so,

[tex]x(x+7)+5x=6.25\\\Rightarrow x^2+7x+5x=6.25\\\Rightarrow x^2+12x-6.25=0\\\Rightarrow 100x^2+1200x-625=0\\\Rightarrow x=\dfrac{-1200\pm \sqrt{1200^2-4\times100\left(-625\right)}}{2\times100}\\\Rightarrow x=0.5,-12.5[/tex]

Learn more about area:

https://brainly.com/question/25292087