An equilateral triangle has a side length of 7 cm. If a perpendicular is dropped from a corner, what is the length of the perpendicular?

6.06cm

Step-by-step explanation:

An equilateral triangle is a triangle that has all its sides equal. If the given  equilateral triangle has a side length of 7 cm, then all its sides are 7cm each. To get the length of the perpendicular dropped from a corner. we will use the Pythagoras theorem.

According to the theorem,

hyp² = opp²+adj²

Lets take the height as the opposite side of one of the right angled triangle as shown in the attachment.

hyp = 7cm and adj = 7/2 = 3.5cm

opp² = 7² - 3.5²

opp² = 49 - 12.25

Opp = √36.75

Opp = 6.06cm

This shows that the length of the perpendicular is 6.06m