Final answer:
The perpendicular dropped from a corner of an equilateral triangle is 7/√3 cm or 7√3/3 cm when rationalized, based on the properties of 30-60-90 right triangles.
Step-by-step explanation:
To find the length of the perpendicular dropped from a corner of an equilateral triangle with a side length of 7 cm, we can use the properties of 30-60-90 right triangles. The perpendicular from a corner to the opposite side in an equilateral triangle divides it into two 30-60-90 right triangles, and in such a triangle, the lengths of the sides are in the ratio 1:√3:2.
The longest side (the hypotenuse) in this case is equal to the side of the equilateral triangle, which is 7 cm. So, the side opposite the 60° angle, which is the perpendicular we want to find, is √3 times shorter than the hypotenuse. Therefore, the length of the perpendicular is 7/√3 cm or 7√3/3 cm when rationalized.