Question

the points q, r, s and t all lie on the same line segment, in that order, such that the ratio of qr : rs : st is equal to 1 : 1 : 3. if qt = 10, find rt.

Explanation:

Step1: Calculate the total number of parts

The ratio of $QR:RS:ST = 1:1:3$, so the total number of parts is $1 + 1+3=5$.

Step2: Find the length of one - part

Since $QT = 10$ and there are 5 parts in total for $QT$, the length of one part is $\frac{QT}{5}=\frac{10}{5} = 2$.

Step3: Calculate the number of parts for $RT$

$RT$ consists of $RS + ST$. The number of parts for $RS$ is 1 and for $ST$ is 3, so the number of parts for $RT$ is $1 + 3=4$.

Step4: Calculate the length of $RT$

Since one part is 2 and $RT$ has 4 parts, then $RT=4\times2 = 8$.

Answer:

$8$