Question

furniture ladd is rearranging his furniture. he wants his couch to sit along the 20 - foot wall, labeled a - c 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 1:4. what distance from the left side of the wall should ladd place the left side of his couch? o 4 ft o 5 ft o 10 ft o 16 ft

Explanation:

Step1: Set up the ratio - distance relationship

Let the distance from the left - hand side of the wall to point B be $x$ feet. Then the distance from point B to the right - hand side of the wall is $20 - x$ feet. Given that the ratio of $AB$ to $BC$ is $1:4$, we can write the equation $\frac{x}{20 - x}=\frac{1}{4}$.

Step2: Cross - multiply the equation

Cross - multiplying the equation $\frac{x}{20 - x}=\frac{1}{4}$ gives us $4x=20 - x$.

Step3: Solve for $x$

Add $x$ to both sides of the equation $4x=20 - x$: $4x+x = 20$, so $5x=20$. Then divide both sides by 5: $x = 4$.

Answer:

4 ft