A rectangle’s width is one-sixth of
its length. Given that the rectangle’s width is
nine inches, determine its length.
We will answer this question by
firstly drawing a diagram and then setting up a one-step linear equation. Let’s consider a rectangle with
width 𝑊-inches and length 𝐿-inches. We’re told in the question that the
width is one-sixth of the length. The word “of” in mathematics means
multiply. So 𝑊 is equal to one-sixth
multiplied by 𝐿. This in turn can be written as 𝑊
equals one-sixth 𝐿 or 𝐿 divided by six.
In this particular question, we’re
told that the rectangle’s width is nine inches. We can substitute this into our
equation so that nine is equal to one-sixth 𝐿. This is the same as nine is equal
to 𝐿 divided by six. In order to solve this equation, we
need to perform the same operation on both sides of the equal sign. In this case, we will multiply by
six as multiplying by six is the opposite or inverse of dividing by six.
On the left-hand side, six
multiplied by nine or nine multiplied by six is equal to 54. On the right-hand side, the sixes
cancel. And we’re just left with 𝐿. As 𝐿 is equal to 54, we can
conclude that the length of the rectangle is 54 inches. We can check this answer by working
out one-sixth of 54. As this is equal to nine, which was
the rectangle’s width, we know that our answer of 54 inches is correct.