An equilateral triangle has an altitude that measures 6√3 cm. What is the perimeter of this triangle?

An equilateral triangle has an altitude that measures 6√3 cm. What is the perimeter of this triangle?

Answers (1)

The altitude of an equilateral triangle divides it into two 30°-60°-90° triangles where the hypotenuse is the side of the equilateral triangle and the altitude is the longer leg. In a 30°-60°-90°, the longer leg is √3 times the shorter leg and the hypotenuse is 2 times the shorter leg.
If x is the side (hypotenuse) and y is the shorter leg, we write: x=2y
Also, \(\displaystyle{6}√{3}=√{3}\cdot{y}\)
Hence, the side length of the equilateral triangle is:
x=2(6)=12 cm
So, its perimeter is: P=3(12)=36 cm

Relevant Questions

asked 2021-01-31
What is the perimeter of the triangle below, to the nearest tenth of an inch, if each square on the grid measures 8 inches on each side?
asked 2021-02-01
One side of an equilateral triangle is given. Solve for the other sides.
3 ft
1 in.
93 m
8.4 yd
asked 2021-01-23
equilaterat triangle has sides of 20 to nearest tenth what is altitude of triangle
asked 2020-11-06
‘Rewrite the Jofinition “An equilateral triangle has three sides vrite the definihon fv, biconditional.
asked 2021-01-13
The drawing shows a uniform electric field that points in the negative y direction; the magnitude of the field is 5300 N/C.Determine the electric potential difference (a) VB - VA between points A and B, (b) VC - VB between points B and C, and (c) VA - VB between points C and A.
A-C is 10.0cm, b-c is 8.0 cm, a-b is 6.0 cm. They are all in a right triangle shape. With angle b having the 90 degree angle, and electric potential is pointing down. This is problem 56 in 7th edition.
asked 2021-01-13
The sides of a triangle are 5.2 cm, 6.3 cm and 9.4 cm, each correct to the nearest millimetre. Calculate the lower bound of the perimeter of the triangle
asked 2021-01-16
The length of the base of an isosceles triangle is x. The length of a leg is 2x - 6. The perimeter is 53. Find x.
asked 2020-12-30
Jamie was supposed to have completed a portfolio of geometric constructions during spring break. She started this construction of a triangle center on the first day of her vacation and then forgot about it. Help her complete her portfolio entry. What is the name of the triangle center that Jamie constructed (point X )? What special properties does it have? Compute the volume of the figure at right.
asked 2021-03-08
Peter says the triangle in not an equilateral triangle because neither all the sides nor all the angles are marked as congruent. Do you agree with peter?
asked 2020-12-15
A rectangle with dimensions 21.6 × 12 has a right triangle with a base 9.6 and a height of 7.2 cut out of the rectangle. What is the area of the shaded region?