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Alvita is planning a garden patio to be made from identical square paving stones laid out in a rectangle
measuring 2 stones by y stones.
She finds that when she adds a border of width one stone around the patio, the area of the border is equal
to the original area of the patio.
How many possible values for x are there?

Sagot :

The length of the square paving is the base unit to which the area of the

and patio and the border are evaluated.

Correct response:

  • The possible x-values are; 10, 6, 4, and 3

Which method is used to evaluate the area of the patio?

Let s represent the size of the square paving, we have;

Area of the patio = s·x × s·y = s²·x·y

New area = (2·s + s·x) × (2·s + s·y) = 4·s² + 2·s²·y + 2·x·s² + s²·x·y

Area of the border = 4·s² + 2·s²·y + 2·x·s² = s²·x·y

2·s²·(2 + y + x) = s²·x·y

2·(2 + y + x) = x·y

4 + 2·y + 2·x = x·y

x·y - 2·x = 4 + 2·y

x·(y - 2) = 4 + 2·y

Which by using  gives;

[tex]x = \mathbf{ \dfrac{4 + 2 \cdot y }{y- 2}}[/tex]

By graphing the above equation on MS Excel, we have the following

possible values of x, and y combination; (10, 3) (6, 4), (4, 6), (3, 10).

Therefore;

  • The possible values of x are; 10, 6, 4, and 3

Learn more about equations here:

https://brainly.com/question/20475360

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