Question

11. A landscaper is designing a rectangular garden, which will be 5.00 m

wide by 6.25 m long. She has enough crushed rock to cover an area
of 6.0 m² and wants to make a uniform border around the garden.
How wide should the border be, if she wants to use all the crushed
rock?

Answer 1

9514 1404 393

Answer:

25.5 cm

Explanation:

If the walk is x meters wide, it adds 2x to the overall length and width. Then the area of the walkway is ...

(2x +5)(2x +6.25) -(5)(6.25) = 6

4x^2 +22.5x = 6 . . . . simplify left side

4x^2 +22.5x -6 = 0 . . . subtract 6 to put into standard form

Using the quadratic formula, the walkway width can be found to be ...

x = (-22.5 +√(22.5² -4(4)(-6)))/(2(4)) = (-22.5 +√602.25)/8

x ≈ 0.25510

The border width should be about 25.5 cm.