Question

From a point in the interior of an equilateral triangle the perpendicular distance of the sides are √3 cm,2√3 cm and 5√3cm.The perimeter of triangle is

Answer 1

Let each side of the equilateral triangle be a.

As shown in the above image, consider the perpendicular distances as

OS = x

OU = y

OT = z

Area of the equilateral triangle PQR =

√3a^2/4 ------------(1)

Area of triangle POQ = 12× PQ × OS = ax2 ------------(2)

Area of triangle POR = 12 × PR × OU

= ay 2 ------------(3)

Area of triangle QOR = 12 × QR × OT

= a2

------------(4)

Area of triangle PQR = (Area of triangle POQ + Area of triangle POR + Area of triangle QOR)√3a^2/4

=ax^2+ay^2+az^2

√3a^2/4

=x^2+y^2+z^2

√3a^/4

=*x+y+z)^2

a = 2√3(x+y+z) ---- (A) .

This can be used as a general formula for such questions.

Applying the given values,

a = 2√3(x+y+z)

=2√3(√3+2√3+5√3)

=2(1+2+5)

= 16 cm

perimeter = 3a = 48 cm

Hope this helps you ✌️✌️☺️☺️❤️