Question

these triangles are similar. z = ___ options: 15, 18, 20

Explanation:

Step1: Identify similarity ratio

The first triangle has side length 5, the second has corresponding side 20. The ratio is $20\div5 = 4$.

Step2: Apply ratio to find z

The first triangle's side (equal to 5) corresponds to z in the second. So $z = 5\times4 = 20$? Wait, no, wait. Wait the first triangle is equilateral (all sides 5), the second is also equilateral (since two sides are 20 and z, so similar implies all sides proportional). Wait, the first triangle: sides 5,5,5. Second: 20,20,z? Wait no, the first triangle has sides 5,5,5 (equilateral), the second has two sides 20 and z, and base 20? Wait, no, looking at the diagram: first triangle: three sides 5. Second triangle: two sides 20 and z, and base 20? Wait, no, the first triangle: left side 5, right side 5, base 5. Second triangle: left side 20, right side z, base 20. Since they are similar, the ratio of corresponding sides is equal. So ratio of left sides: 20/5 = 4. So right side z should be 54 = 20? Wait but the options include 20. Wait, but let me check again. Wait the first triangle is 5,5,5 (equilateral), second is 20,20,z? Wait no, maybe the first triangle has sides 5,5,5, second has sides 20, z, 20. So since similar, the ratio is 20/5 = 4, so z = 54 = 20. So z is 20.

Answer:

20