Two triangles are similar, with areas measuring 12 cm² and 48 cm² respectively. If the height of the smaller triangle is 2.1 cm, what is the height of the larger triangle corresponding to it?

Explanation

For similar triangles, the ratio of their areas equals the square of the ratio of their corresponding heights. Given areas 12 and 48, the ratio is 12/48 = 1/4. Let h be the height of the larger triangle, then (2.1 / h)² = 1/4, which implies h² = 4 × (2.1)². Taking the square root, h = 2 × 2.1 = 4.2 cm.