Thread: Lengths of triangle

Two triangles are similar. The lengths of the sides of the smaller triangle are 3, 5, and 6, and the lengths of the longest side of the larger triangle is 18. What is the perimeter of the larger triangle.

1) 14
2) 18
3) 24
4) 42

Explain.

Originally Posted by aznmartinjai

Two triangles are similar. The lengths of the sides of the smaller triangle are 3, 5, and 6, and the lengths of the longest side of the larger triangle is 18. What is the perimeter of the larger triangle.

1) 14
2) 18
3) 24
4) 42

Explain.

since the two triangles are similar, the lengths of their sides are proportional. the longest side of the small triangle is 6, and the longest side of the large triangle is 18

note that 18 = 3*6, so the larger triangle is larger than the small triangle by a factor of 3, it means that the lengths of the other sides of the larger triangle are 3*3 = 9 and 3*5 = 15

so all the sides of the large triangle are 9, 15 and 18, use these to find the perimeter