A square chess board has an area of 16 – 24g + 9g² square centimeters. What is the length of its side?

Solution:

A = s²

16 – 24g + 9g² = s²

(4 – 3g)² = s²

s = (4 – 3g)

Answer:

The length of its side is 4 – 3g centimeters.

A rectangular lot has an area of x² + x - 6 square meters. What is the ideal dimension of this lot?

Solution:

Factor x² + x - 6. Each factor will be the dimensions of the rectangular lot.

x² + x - 6 = (x + 3)(x - 2)

Answer:

The dimension of the lot is (x + 3) meters by (x - 2) meters.

Answer:

1. 16 - 24g + 9g²

Standard Form : 9g² - 24g + 16

Rewrite in exponential form :

3²g²- 2(3g)(4) + 4²

Combine terms with equal exponents :

(3g)² - 2(3g)(4) + 4²

Using a² - 2ab + b² = (a - b)², factor :

(3g - 4) ²

Therefore, the length of one side is 3g - 4.

2. x² + x - 6

Factor :

(x + 3)(x - 2)

Therefore, the dimensions of the lot are x + 3 meters by x - 2 meters.