In triangle ABC, DE is parallel to AC. Side AD measures 5.3 units, side DB measures 8.0 units, and DE measures 4.8 units. What is the measure of AC?
by similar triangles,
AC/AB = DE/DB
AC/(5.3+8.0) = 4.8/8.0
AC = 7.98
To find the measure of AC, we can use the concept of similar triangles. Since DE is parallel to AC, triangle ADE and triangle ABC are similar triangles.
Similar triangles have proportional side lengths. Therefore, we can set up a proportion to find the measure of AC.
Let's denote the measure of AC as x. The proportion can be set up as follows:
AD/DE = AB/AC
Plugging in the given values:
5.3/4.8 = 8.0/x
To solve for x, we cross-multiply:
5.3x = 4.8 * 8.0
5.3x = 38.4
Dividing both sides by 5.3:
x = 38.4/5.3
x ≈ 7.25
Therefore, the measure of AC is approximately 7.25 units.