Triangle ABC and triangle XYZ are similar. If AB, BC, and AC are 7 inches, 9 inches, and 10 inches respectively, and
XY is 9 inches, find XZ to the nearest tenth of an inch.
YZ= 11.6
xz= 12.9
To find the length of XZ, we can set up a proportion using the ratios of corresponding sides in similar triangles.
The ratio of the sides of triangle ABC to triangle XYZ can be written as:
AB / XY = BC / YZ = AC / XZ
Substituting the given values:
7 / 9 = 9 / YZ = 10 / XZ
To find XZ, we need to solve for it in the proportion. Cross-multiplying, we get:
7 * XZ = 9 * 10
7XZ = 90
Dividing both sides by 7, we find that:
XZ = 90 / 7
XZ ≈ 12.8571
Rounded to the nearest tenth:
XZ ≈ 12.9 inches