Question

the points f, g, h and i all lie on the same line segment, in that order, such that the ratio of fg : gh : hi is equal to 5 : 5 : 1. if fi = 33, find gi.

Explanation:

Step1: Calculate the total number of parts

The ratio of $FG:GH:HI = 5:5:1$, so the total number of parts is $5 + 5+1=11$ parts.

Step2: Find the length of one - part

Since $FI$ is the whole line - segment and $FI = 33$, and $FI$ is composed of 11 parts. Then the length of one part is $\frac{33}{11}=3$.

Step3: Calculate the number of parts of $GI$

The line - segment $GI$ is composed of $GH + HI$. The number of parts of $GH$ is 5 and the number of parts of $HI$ is 1, so the number of parts of $GI$ is $5 + 1=6$ parts.

Step4: Calculate the length of $GI$

Since one part is 3 and $GI$ has 6 parts, then $GI=6\times3 = 18$.

Answer:

18