Answer:
Step-by-step explanation:
We can find that angle P = 180 - 30 - 30 = 120.
Constructing an angle bisector that divides P into two 60 degree angles and meets at point S in RQ, also dividing RQ into 2 equal segments, we can find the area because the ratio of the sides of a 30-60-90 degrees triangle is 1: sqrt3: 2.
Making an equation where x = PS and RS = x[tex]\sqrt3[/tex] and PR = 2x, we get:
[tex]\frac{{x}\cdot{x\sqrt3}}{2}=40[/tex]
[tex]x\cdot x\sqrt3=80[/tex]
[tex]x^2\sqrt3=80[/tex]
[tex]x^2=\frac{80}{\sqrt3}[/tex]
[tex]x=\sqrt\frac{80}{\sqrt3}[/tex]
Simplifying this in a calculator, we get:
x = 6.79617697939
Now we know that x = 6.79617697939, and PR = 2x, and because PR = PQ, combined they make 4x = 4 x 6.79617697939 = 27.1847079176.
Since RS = [tex]x\sqrt3[/tex], RQ = [tex]2x\sqrt3[/tex] = 2 x 6.79617697939[tex]\sqrt3[/tex] = 13.5923539588[tex]\sqrt3[/tex] = 23.5426476511. Adding 27.1847079176 and 23.5426476511, we get:
50.7273555687
Which is around
50.727
Solution: 50.727 cm
