Question

Find the value of r. A. 24 B. 12 C. 2 D. 3

Answer 1

r = 3

Explanation:

Here Triangle ALR is divided precisely in half by the vertical side LU. The two triangles thus formed are therefore congruent.

Thus, 18 - 2r = 4r, and 6r = 18. Then r = 3.

Answer 2

`\boxed{r=3}`

Explanation:

We can use SAS ≅ SAS congruence to validate that the triangles are similar (both share the same side, have another congruent side, and have a congruent angle).

Because the sides are congruent, set them equal to each other and solve for r.

18 - 2r = 4r

18 = 6r

3 = r ⇒
`\boxed{\bold r = 3}`

Therefore, the answer is D.