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

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.

6mm^3 or .6cm^3

      216

      /   \

  36     6

  /   \     /

6     6   6

factor trees are nice.