## Detailed instructions for solving Problem 7.29

**Solution method**

Indicates the number of stakes to fence the full length

Find polynomials expressing width and length.

Find the polynomial that shows the area of the garden = the length. width

**Detailed explanation**

Because the number of stakes used to fence the entire length of the garden is 20 more than the number of stakes used to fence the full width, the number of stakes used to fence the length is: x + 20

Because each corner of the garden has a stake and two consecutive stakes are inserted 0.1 m apart, so:

The width of the garden is: 0.1 . (x – 1) = 0.1x – 0.1

The length of the garden is: 0.1 . (x + 20 – 1) = 0.1(x + 19) = 0.1x + 1.9

The polynomial for the area of the garden is:

S = (0.1x – 0.1) . (0.1x + 1.9)

= 0.1x . (0.1x + 1.9) – 0, 1. (0.1x + 1.9)

= 0.1x . 0.1x + 0.1x . 1.9 – (0.1.0.1x + 0.1.1.9)

= 0.01x^{2} + 1.9x – (0.01x + 0.19)

= 0.01x^{2} + 1.9x – 0.01x – 0.19

= 0.01x^{2} + 1.89x – 0.19

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