Question

Стороны Треугольника ABC имеют длины 5,7 и 9.Подобен ли треугольник ABC треугольнику MNP если длины его сторон равны 15,21 и 27?

Answer 1

Да. Стороны отличаются в 3 раза. Подобны

Answer 2

Triangle Similarity

The given triangles are triangle ABC with side lengths 5, 7, and 9, and triangle MNP with side lengths 15, 21, and 27. To determine if triangle ABC is similar to triangle MNP, we can compare the ratios of the corresponding sides of the two triangles.

Step 1: Calculate the Ratios of Corresponding Sides

The ratios of the corresponding sides of the two triangles are calculated as follows: - Ratio of side lengths AB to MN - Ratio of side lengths BC to NP - Ratio of side lengths AC to MP

Step 2: Check for Proportionality

If the ratios of the corresponding sides are equal, then the triangles are similar.

Calculation of Ratios

The ratios of corresponding sides are as follows: - AB/MN = 5/15 = 1/3 - BC/NP = 7/21 = 1/3 - AC/MP = 9/27 = 1/3

Conclusion

The ratios of the corresponding sides of triangle ABC to triangle MNP are all equal to 1/3. Therefore, based on the ratio of the side lengths, triangle ABC is similar to triangle MNP.