Question

what are the values of a and b. a=9/2, b=15/2 | a=15/2, b=9/2 | a=16/3, b=15/2 | a=9/2, b=13/2

Answer 1

To solve for a and b, we must create a proportion.

Triangle 10-8-6 is similar to triangle b-6-a, which are both similar to triangle 8+a-10-b.

10/8=b/6
60 = 8b
b = 15/2 = 7.5

8/6=6/a
36=8a
a=4.5

We can confirm by using the Pythagorean theorem:

4.5² + 6² = 7.5²

56.25 = 56.25

The equation is true, so a must equal 4.5 and b must equal 7.5. Choose the first option.

Answer 2

The values of a and b are
`a=9/2`,
`b=15/2`

Explanation:

we know that

If two triangles are similar, then the ratio of its corresponding sides is equal and its corresponding angles are congruent

In this problem the two triangles of the figure are similar, because the corresponding angles are congruent

so

`(6)/(a)=(8)/(6)=(10)/(b)`

First solve for a

`a=6*6/8=9/2`

`b=6*10/8=15/2`