Question

ladd is rearranging his living room furniture. he wants his couch to sit along the 20-ft wall, labeled ac
on the diagram. he would like the left side of his couch to sit at a point b so that the ratio of ab to bc is 1: 4.

Answer 1

Answer:

AB = 4 ft

BC = 16 ft

Step-by-step explanation:

To find the length of AB and BC you need to relate them using equations.

AB + BC = 20 ft (from the diagram)

4AB = BC (from your ratio)

Substituting BC = 4AB into AB + BC = 20:

AB + 4AB = 20 ft

5AB = 20 ft

AB = 4 ft

Plugging AB = 4 ft into AB + BC = 20 ft:

4 ft + BC = 20 ft

BC = 20 ft - 4 ft

BC = 16 ft

To check this, test both values against the ratio:

AB:BC = 1:4

4:16 = 1:4

1:4 = 1:4

So AB = 4 ft and BC = 16 ft