Question

Calculate the area and the height of an equilateral triangle whose perimeter is 60cm​

Answer 1

Well if the perimeter is 60cm and all sides are equal then each side is 20cm.

This would mean that a line representing the height of the triangle will bisect the far side, giving us 2 triangles with 20cm hypotenuses and one side of 10cm and 1 shared side representing the height.

Then,

H² = B² + P²

(20)² = (10)² + P²

400 = 100 + P²

400-100 = P²

300 = P²

P = √300

P = 17.32cm

Area = Base x Height / 2

        = 20cm x 17.30cm

        = 346.4 cm²

Answer 2

Answer:

Area = 100$\sqrt{3}$$cm^{2}$

Height = 10$\sqrt{3}cm$

Step-by-step explanation:

Perimeter = 60cm

3a = 60cm

a = (60/3)cm

a = 20cm

Area = $\frac{\sqrt{3} }{4} *a^{2}$

Area = $\frac{\sqrt{3}}{4}*20^{2}$

Area = $\frac{\sqrt{3}}{4}*400$

Area = 100$\sqrt{3}cm^{2}$

1/2 * b * h = 100$\sqrt{3}$

1/2 * 20 * h =100$\sqrt{3}$

h = (100$\sqrt{3}$)/10

h = 10$\sqrt{3}$cm