Question

the points g, h, i and j all lie on the same line segment, in that order, such that the ratio of gh : hi : ij is equal to 3 : 3 : 2. if gj = 24, find hj.

Explanation:

Step1: Find the total parts of the ratio

The ratio of \( GH:HI:IJ \) is \( 3:3:2 \). To find the total number of parts, we add the parts of the ratio: \( 3 + 3 + 2 = 8 \) parts.

Step2: Find the value of one part

We know that the length of \( GJ \) is the sum of \( GH \), \( HI \), and \( IJ \), so \( GJ = 24 \) corresponds to 8 parts. To find the value of one part, we divide the total length by the total number of parts: \( \frac{24}{8}=3 \).

Step3: Find the length of \( HJ \)

\( HJ \) is the sum of \( HI \) and \( IJ \). From the ratio, \( HI \) is 3 parts and \( IJ \) is 2 parts, so \( HJ \) has \( 3 + 2 = 5 \) parts. Since one part is 3, the length of \( HJ \) is \( 5\times3 = 15 \).

Answer:

\( 15 \)