### All ACT Math Resources

## Example Questions

### Example Question #173 : Plane Geometry

Two similiar triangles have a ratio of perimeters of .

If the smaller triangle has sides of 3, 7, and 5, what is the perimeter of the larger triangle.

**Possible Answers:**

**Correct answer:**

Adding the sides gives a perimeter of 15 for the smaller triangle. Multipying by the given ratio of , yields 52.5.

### Example Question #2 : Acute / Obtuse Triangles

Two similiar triangles exist where the ratio of perimeters is 4:5 for the smaller to the larger triangle. If the larger triangle has sides of 6, 7, and 12 inches, what is the perimeter, in inches, of the smaller triangle?

**Possible Answers:**

18

23

20

25

**Correct answer:**

20

The larger triangle has a perimeter of 25 inches. Therefore, using a 4:5 ratio, the smaller triangle's perimeter will be 20 inches.

### Example Question #173 : Geometry

Two similar triangles' perimeters are in a ratio of . If the lengths of the larger triangle's sides are , , and , what is the perimeter of the smaller triangle?

**Possible Answers:**

**Correct answer:**

1. Find the perimeter of the larger triangle:

2. Use the given ratio to find the perimeter of the smaller triangle:

Cross multiply and solve:

### Example Question #176 : Plane Geometry

There are two similar triangles. Their perimeters are in a ratio of . If the perimeter of the smaller triangle is , what is the perimeter of the larger triangle?

**Possible Answers:**

**Correct answer:**

Use proportions to solve for the perimeter of the larger triangle:

Cross multiply and solve:

### Example Question #174 : Geometry

Two similar triangles have perimeteres in the ratio . The sides of the smaller triangle measure , , and respectively. What is the perimeter, in meters, of the larger triangle?

**Possible Answers:**

**Correct answer:**

Since the perimeter of the smaller triangle is , and since the larger triangle has a perimeter in the ratio, we can set up the following identity, where the perimeter of the larger triangle:

In cross multiplying this identity, we get . We can now solve for . Here, , so the perimeter of the larger triangle is .

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