find the median and altitude of a equilateral triangle whose side is 60 cm
Answers
Answer:
Given, perimeter of equilateral triangle is 60cm.
Perimeter of equilateral triangle=60cm
3× side =60
∴ side =
3
60
=20cm.
Area of equilateral triangle =
4
3
(side)
2
=
4
3
×20
2
=100
3
cm
2
=173.2cm
2
Height of equilateral triangle =
2
3
(side)
=
2
3
×20
=10
3
cm=17.32cm
Step-by-step explanation:
Answer:
hi nice to meet u ...
Step-by-step explanation:
There is a lot of geometry to consider here and I'm going to give you all the details.
First, an equilateral triangle is also equiangular. Since the interior angle sum of any triangle is 180°, each angle of an equilateral triangle is 60°.
Next, the definition of an isosceles triangle is a triangle with at least two sides congruent. Thus, an equilateral triangle is also isosceles and therefore all the theorems associated with isosceles triangles also apply to equilateral triangles.
Now, draw an angle bisector dividing one 60° angle into two 30° angles to the opposite side. Now apply this theorem: The bisector of the vertex angle of an isosceles triangle is perpendicular to its base at the base’s midpoint.
Now with all of this put together you conclude that your equilateral triangle can be divided into two adjacent 30–60–90 special right triangles where the side opposite the 60° angle is the height of your equilateral triangle.
We're not done yet.
Now it should be clear that the hypotenuse of your 30–60–90 right triangle is one of the sides of your equilateral triangle and the side opposite the 30° angle is half that length. So let's let b equal the length of the hypotenuse, so 12b is the length of the short side. From what you learned about 30–60–90 right triangles, you know that the long side, the side opposite the 60° angle is equal to the short side times 3–√ and that is your height.
Thus, h=(1/2)b×3–√=(3–√/2)b