Question

answer this quickly 15th

Answer 1

Answer:

a) 42√3

Step-by-step explanation:

area of the triangle(heron's formula);

S = a+a+a/2

S = 3a/2

A = √3a/2(3a/2-a)(3a/2-a)(3a/2-a)

A = √3a/2(a/2)(a/2)(a/2)

A= a/2 × a/2 × √3

A = √3a²/4

Now, Area of the three triangles formed by the perpendiculars;

Area of triangle = 1/2 × a × 5 + 1/2 × a × 7 + 1/2 × a × 9

                          = 1/2(5a + 7a + 9a)

                         = 1/2(21a) = 21a/2

so, 21a/2 = √3a²/4

21a × 4 = 2 × √3a²

84 = 2√3a²/a

84 = 2√3a

42/√3 = a

a = 42/√3 × √3/√3

a = 42√3/3

a = 14√3

perimeter of equilateral triangle = 3a

= 3 × 14√3

= 42√3