Question

furniture nico is rearranging his furniture. he wants his couch to sit along the 20 - foot wall, labeled $overline{ac}$ on the diagram. he wants the left side of his couch to sit at a point $b$ so that the ratio of $ab$ to $bc$ is $1:3$. what distance from the left side of the wall should nico place the left side of his couch?

Explanation:

Step1: Determine the total number of parts.

The ratio of $AB$ to $BC$ is $1:3$, so the total number of parts is $1 + 3=4$.

Step2: Calculate the length of one - part.

The length of the wall $AC = 20$ feet. Since there are 4 parts in total, the length of one part is $\frac{20}{4}=5$ feet.

Step3: Find the length of $AB$.

The left - hand side of the couch is at point $B$ and $AB$ represents 1 part. So the distance from the left - hand side of the wall to the left - hand side of the couch (the length of $AB$) is 5 feet.

Answer:

5 feet