Question

what is the measure of one side of the square if its area is 100x² - 160x + 64?

Answer 1

The Area of a Square is the square of the measure of one side of the square.

Hence, given the expression for the area of a square, express the given area as the square of an expression to get the measure of one side.

The given expression is:

$100x^2-160x+64$

Rewrite the expression as:

$\begin{gathered} 10^2x^2-(2\times10\times8)x+8^2 \\ =(10x)^2-(2\times10x\times8)+8^2 \end{gathered}$

Recall the binomial expansion:

$(a-b)^2=a^2-2ab+b^2$

Substituting a=10x and b=8, it follows that the expression becomes:

$(10x-8)^2$

Since the area of a square is the square of the measure of one side, it follows that the measure of one side from the given expression is 10x-8.