Question

"Two triangles are similar. The sides of the first triangle are 5, 10, and 15. The largest side of the second triangle is 20. Find the perimeter of the second triangle."

A. 30
B. 40
C. 45
D. 60

Answer 1

Two similar triangles with sides 5, 10, 15 and a scale factor of 4/3. Perimeter of the second triangle is 40 units.

Step-by-step explanation:

Two triangles are similar if their corresponding angles are equal and their corresponding sides are in proportion. Let's find the scale factor between the two triangles by comparing their longest sides. The longest side of the first triangle is 15 units and the longest side of the second triangle is 20 units. The scale factor is 20/15 = 4/3. This means that every side of the second triangle is 4/3 times the length of the corresponding side of the first triangle.

Since the perimeter is the sum of all the sides of a triangle, the perimeter of the second triangle would be 4/3 times the perimeter of the first triangle. The perimeter of the first triangle is 5 + 10 + 15 = 30 units. Therefore, the perimeter of the second triangle is (4/3) * 30 = 40 units.