To find the lengths of FG, GH, and HJ in quadrilateral FGHJ, given that quadrilateral ABCD is similar to FGHJ with a ratio of similitude of 7:11 and FJ=11, AB=2x, BC=3x, CD=4x, and AD=x, follow these steps:
1. Set up the ratio of similitude: (ABCD side)/(FGHJ side) = 7/11.
2. Use the given side lengths of FGHJ (FJ) and ABCD (AB, BC, CD, AD) to find the corresponding side lengths in FGHJ.
a. For FG (corresponding to AB), the ratio is (2x)/FG = 7/11. Solve for FG:
11 * (2x) = 7 * FG
22x = 7 * FG
FG = 22x / 7
b. For GH (corresponding to BC), the ratio is (3x)/GH = 7/11. Solve for GH:
11 * (3x) = 7 * GH
33x = 7 * GH
GH = 33x / 7
c. For HJ (corresponding to CD), the ratio is (4x)/HJ = 7/11. Solve for HJ:
11 * (4x) = 7 * HJ
44x = 7 * HJ
HJ = 44x / 7
So, FG = 22x / 7, GH = 33x / 7, and HJ = 44x / 7.