An isosceles triangle has side lengths 8 cm, 8 cm and 10 cm.  The longest side of a similar triangle is 25 cm. What is the perimeter of the larger triangle, in centimeters?
I know that similar triangles have proportional side lengths, so I can use a ratio to compare the corresponding sides of the two triangles. Let x be the length of one of the congruent sides of the larger triangle, then I can write the ratio 8 : 10 = x : 25. To solve for x, I can cross-multiply and get 10x = 200, so x = 20. Now I know the lengths of all three sides of the larger triangle: 20 cm, 20 cm and 25 cm. The perimeter of a triangle is the sum of its side lengths, so the perimeter of the larger triangle is 20 + 20 + 25 = 65 cm.

