Right triangle ABC is similar to triangle XYZ. If XY = 35 cm,
YZ = 70 cm, and AB = 5 cm, then what is the length of line segment BC?
AB/XY = BC/YZ,
5/35 = BC/70,
Multiply both sides by 70:
BC = 70*5/35 = 10 cm.
To determine the length of line segment BC, we can use the concept of similarity between triangles.
In similar triangles, corresponding sides are proportional. This means that if the ratio of corresponding sides in two triangles is the same, then the triangles are similar.
Given the triangle similarity between ABC and XYZ, we can set up the proportion:
AC / XY = BC / YZ
Plugging in the given values:
AC / 35 = 5 / 70
Now, we can solve for AC:
AC = (5 / 70) * 35
AC = 5 * 0.5
AC = 2.5 cm
Therefore, the length of line segment BC is 2.5 cm.
To find the length of line segment BC, we can use the concept of similar triangles.
In similar triangles, corresponding sides are proportional.
In triangle ABC, we have AB = 5 cm as given.
Now we compare the corresponding sides of the two triangles:
AB to XY,
BC to YZ, and
AC to XZ.
Since triangle ABC is similar to triangle XYZ, we can set up a proportion using the corresponding sides:
AB/XY = BC/YZ
Plugging in the given values, we get:
5/35 = BC/70
Now we can solve for BC:
5 * 70 = BC * 35
350 = 35BC
BC = 350 / 35
BC = 10 cm
Therefore, the length of line segment BC is 10 cm.