Triangle abc and triangle xyz are similar. If ab,bc, and ac are 10, 13, and 14 inches respectively, and xy is 11 inches, find xz to the nearest tenth of an inch.
(11/10)14
ab:xy = 10:11
So, other sides are in the same ratio
ac/xz = 10/11
14/xz = 10/11
xz = 15.4
To solve this problem, we can use the property of similar triangles, which states that the corresponding sides of similar triangles are proportional.
Given that triangle ABC is similar to triangle XYZ, we can set up the following proportion:
AB/XY = BC/XZ
Substituting the given values, we have:
10/11 = 13/XZ
Now we can solve for XZ by cross-multiplying:
10 * XZ = 11 * 13
10XZ = 143
Dividing both sides by 10:
XZ = 14.3 inches
Therefore, XZ is approximately 14.3 inches to the nearest tenth of an inch.