Area of a painting. A rectangular painting with a width of
x centimeters has an area of x2 � 50x square centimeters.
Find a binomial that represents the length. See the accompanying
figure.
To find the binomial that represents the length of the rectangular painting, we need to use the given information that the area of the painting is \(x^2 - 50x\) square centimeters.
We know that the formula for the area of a rectangle is \(\text{Area} = \text{Length} \times \text{Width}\).
So, we can set up the equation: \(x^2 - 50x = \text{Length} \times x\).
Now, we can divide both sides by \(x\) to solve for the length:
\(\dfrac{x^2 - 50x}{x} = \text{Length}\).
Simplifying the expression:
\(\text{Length} = x - 50\).
Therefore, the binomial that represents the length of the rectangular painting is \(x - 50\).