A figure.Short description, A figure.,Long description,
The figure shows triangle A B C.
The measure of side B C is 63 mm. The measure of side C A is 36 mm.
Point E lies on side A B. The distance from A to E is 30 mm.
Point D lies on side C A.
Segment D E is parallel to side B C. The measure of segment D E is 42 mm.
Question
What is the length of segment A B?
Answer options with 4 options
A.
39 millimeters
B.
41 millimeters
C.
45 millimeters
D.
51 millimeters
To find the length of segment AB, we can use the fact that segment DE is parallel to side BC. This means that triangle ABC and triangle ADE are similar by the AAA (angle-angle-angle) similarity criterion.
From triangle ABC, we know that BC = 63 mm and CA = 36 mm.
Since triangle ABC and triangle ADE are similar, we can set up the following proportion:
AB / DE = CA / BC
Substituting the given values, we get:
AB / 42 = 36 / 63
Cross-multiplying, we have:
AB = (42 * 36) / 63
AB ≈ 24 mm
Therefore, the length of segment AB is approximately 24 mm.
None of the provided answer options match the correct answer.