Video Transcript
Find the missing side length of the
following rectangle.
In this question, we are asked to
find the missing side length of a rectangle. To do this, we are given the width
of the rectangle and its area in terms of an unknown 𝑥. If we say that the missing side has
a length of 𝑙, then we can recall that the area of a rectangle is its width
multiplied by its length. So we have 𝑙 times four 𝑥 is
equal to 24𝑥 squared.
We know that 𝑥 is nonzero since
its width is four 𝑥, so we can divide both sides of the equation by four 𝑥. This gives us that 𝑙 is equal to
24𝑥 squared over four 𝑥. We can then cancel the shared
factor of four in the numerator and denominator to get six 𝑥 squared over 𝑥.
We can simplify this expression by
recalling that the quotient rule for exponents tells us that for a nonzero base 𝑏,
𝑏 raised to the power of 𝑚 over 𝑏 raised to the power of 𝑛 equals 𝑏 raised to
the power of 𝑚 minus 𝑛. We can then rewrite the 𝑥 in the
denominator so that we can apply the quotient rule to obtain six 𝑥 raised to the
power of two minus one, which we can evaluate is six 𝑥.
We can verify that this is correct
by multiplying the length and width of the rectangle. We have four 𝑥 times six 𝑥 is
equal to four times six multiplied by 𝑥 times 𝑥, which is equal to 24𝑥
squared.
