Use the image to answer the question.
An illustration shows a larger triangle upper A upper B upper C and a smaller triangle upper D upper E upper F, with labeled sides. On the first triangle, side upper B upper C is the base labeled as 36, side upper A upper B is the hypotenuse labeled as x, and vertical side upper A upper C is on the left and is not labeled. On the second triangle, side upper E upper F is the base labeled as 3, side upper D upper E is the hypotenuse labeled as 6, and vertical side upper D upper F is on the left and is not labeled.
If ΔABC is similar to ΔDEF , and BC= 36, EF= 3, and DE= 6, what is the measure of AB ?
(1 point)
The measure of AB can be found using the concept of similarity of triangles. Since ΔABC is similar to ΔDEF, the corresponding sides of the triangles are proportional.
Given: BC = 36 and EF = 3
Let x be the measure of AB.
By the proportional relationship, we can set up the following proportion:
BC/EF = AB/DE
Substituting the given values:
36/3 = x/6
Now, we can solve for x:
36 * 6 = 3 * x
216 = 3x
x = 72
Therefore, the measure of AB is 72.