Question

Shakil draws an equilateral triangle PQR. I draw three perpendiculars from a point inside
of that equilateral triangle on three sides, of which lengths are 10cm, 12cm and 8cm. Let us
write by calculating the area of triangle.​

Answer 1

Given : Drawn three perpendiculars from a point inside  of that equilateral triangle on three sides, of which lengths are 10cm, 12cm and 8cm

To find : area of triangle.​

Solution:

Let say side of Equilateral triangle = a  cm

Area of triangle = (√3 / 4)a²  cm²

Area of triangle = (1/2) * a * 10  + (1/2)*a *12  + (1/2)*a * 8

= (1/2) *a ( 10 + 12 + 8)

= (1/2) * a * 30

= 15a   cm²

(√3 / 4)a²  = 15a

=> a = 60/√3

=> a = 20√3

Area of triangle = 15a  =  15 (20√3)  = 300√3  cm²

= 519.6 cm²

Learn more:

An equilateral triangle and a right-angled triangle, having the same ...

https://brainly.in/question/17654026

Find the area of an equilateral triangle having altitude h cm.the ...

https://brainly.in/question/18252568