Question

What are the values of a and b?

Answer 1

Answer:

D

Step-by-step explanation:

These two triangles are similar triangles. The two angles marked are the same and the two angles at the intersection where you see the square are also the same, making it clear that the last angle must be the same as well.

Therefore,

length 8 from the top triangle is similar to length 6 on the bottom triangle,

length 10 from the top is similar to b on the bottom triangle,

length 6 from the top is similar to a on the bottom.

To find the ratio of similarity, you would compare the length 8 to length 6, and divide them. 8/6 = 1.33333

Now that you've found the proportionality constant, you divide the other two lengths on the top triangle with the constant to get b and a.

b = 10/1.3333 = 7.5

a = 6/1.3333 = 4.5

Therefore, the answer is D: a = 9/2, b = 15/2.