Question

1. the points h, i, j and k all lie on the same line segment, in that order, such that the ratio of hi : ij : jk is equal to 1 : 2 : 2. if hk = 135, find hj

Explanation:

Step1: Find the total number of parts

The ratio of $HI:IJ:JK = 1:2:2$, so the total number of parts is $1 + 2+2=5$.

Step2: Find the length of one - part

Since $HK$ is the whole line - segment and $HK = 135$, and there are 5 parts in total, the length of one part is $\frac{135}{5}=27$.

Step3: Find the length of $HJ$

$HJ$ consists of $HI$ and $IJ$. The number of parts for $HJ$ is $1 + 2=3$. So the length of $HJ$ is $3\times27 = 81$.

Answer:

81