Question

The area of the square is 16x^2 -40xy + 25y^2 square units. What is the side of the square?

Answer 1

Given:

`Area=16x^2-40xy+25y^2`

To determine the side of the square, we first note that formula of the area of a square is:

`Area=(Side)^2`

Hence,

`Side=√(Area)`

Now, we solve for the side of the square:

`\begin{gathered} S\imaginaryI de=√(Area) \\ S\imaginaryI de=√(16x^2-40xy+25y^2) \\ Simplify\text{ and rearrange} \\ S\mathrm{i}de=√((4x-5y)^2) \\ \end{gathered}`

Then, we apply the radical rule:

`\sqrt[n]{a^n}=a,\text{ assuming a}\ge0`

So,

`\begin{gathered} S\imaginaryI de=√((4x-5y)^2) \\ S\mathrm{i}de=4x-5y \end{gathered}`

Therefore, the side of the square is:

`4x-5y`