Find the missing side in each pair of similar triangles.

Let’s solve each problem one by one. Since the figures are similar, their corresponding sides are proportional — meaning we can set up ratios to find the missing side.

---

Problem 1:

Left triangle has sides 12 and 20.
Right triangle has sides 3 and x.

We match the sides:
The side of length 12 corresponds to the side of length 3 (both are the left slanted sides).
So the ratio is:
12 / 3 = 4 → That means the big triangle is 4 times bigger than the small one.

Now, the base of the big triangle is 20, so the base of the small triangle should be:
20 ÷ 4 = 5

✔ So, x = 5

---

Problem 2:

Small triangle: sides x and 1
Big triangle: sides 9 and 3

Match the vertical sides: 1 corresponds to 3 → ratio is 1/3
That means the small triangle is 1/3 the size of the big one.

So, the horizontal side x should be 1/3 of 9:
x = 9 × (1/3) = 3

✔ So, x = 3

---

Problem 3:

Small triangle: sides x and 4
Big triangle: sides 8 and 16

Match the long slanted sides: 4 corresponds to 16 → ratio is 4/16 = 1/4
So small triangle is 1/4 the size of the big one.

Then, the other side x should be 1/4 of 8:
x = 8 × (1/4) = 2

✔ So, x = 2

---

Problem 4:

Small triangle: sides 5 and 4
Big triangle: sides x and 8

Match the bases: 4 corresponds to 8 → ratio is 4/8 = 1/2
So small triangle is half the size of the big one.

Then, the vertical side x should be twice the small triangle’s vertical side:
x = 5 × 2 = 10

✔ So, x = 10

---

Final Answer:
1) 5
2) 3
3) 2
4) 10