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 AB is the hypotenuse of right triangle ABC.
Using the Pythagorean theorem, we have:
AB^2 = BC^2 + CA^2
Substituting the given values, we have:
AB^2 = (63^2) + (36^2)
AB^2 = 3969 + 1296
AB^2 = 5265
Taking the square root of both sides, we get:
AB = √5265
Using a calculator, we find that AB ≈ 72.5
Since none of the answer options match the calculated value, it seems there is either an error in the given lengths or answer options.