Question

Draw triangle POR where the angles are in ratio 1:2:3 Draw triangle ABC similar to triangle PQR whose sides are 1/3 times the side of Triangle PQR​

Answer 1

Answer:

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 = √3a243a24 ------------(1)

 

Area of triangle POQ = 1212 × PQ × OS = ax2ax2 ------------(2)

Area of triangle POR = 1212 × PR × OU = ay2ay2 ------------(3)

Area of triangle QOR = 1212 × QR × OT = az2az2 ------------(4)

Area of triangle PQR = (Area of triangle POQ + Area of triangle POR + Area of triangle QOR)

√3a24=ax2+ay2+az23a24=ax2+ay2+az2

√3a4=x2+y2+z23a4=x2+y2+z2

√3a4=x+y+z23a4=x+y+z2 

a = 2√3(x+y+z)23(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)23(x+y+z)=23(3+23+53)=2(1+2+5)= 16 cm