Question

What are the dimensions of a rectangle whose area is represented by the expression 49x^2-16?Length:_________________Width:__________________

Answer 1

Given :

The area of the rectangle = A

`A=49x^2-16`

The given expression is the difference between two squares

`\begin{gathered} 49x^2=7x\cdot7x \\ 16=4\cdot4 \end{gathered}`

So, factor the expression of the area:

`A=(7x+4)\cdot(7x-4)`

So, the answer will be ;

`\begin{gathered} \text{Length }=7x+4 \\ \text{Width =7x-4 } \end{gathered}`