Mathematics Question and Solution
Calculating Parallelogram ABCD Perimeter.
4² = x²+y²-2xycos60
16 = x²+y²-xy
16+xy = x²+y² --- (1).
6² = x²+y²-2xycos120
36 = x²+y²+xy
36-xy = x²+y² --- (2).
Equating (1) and (2).
16+xy = 36-xy
2xy = 20
xy = 10
x = 10/y --- (3).
Calculating y.
Substituting (3) in (1).
16+(10/y)y = (10/y)²+y²
26 = (100/y²)+y²
26y² = 100+y⁴
y⁴-26y²+100 = 0
(y²-13)² = -100+(-13)²
(y²-13)² = 169-100
y² = 13±√(69)
It implies;
y ≠ √(13-√(69)) units.
y = √(13+√(69)) units.
y = 4.61590986295 units.
It implies;
Calculating x.
At (3), x = 10/y.
And y = √(13+√(69)) units.
x = 10/√(13+√(69)) units.
x = √(13-√(69)) units.
x = 2.16642012017 units.
It Implies, Parallelogram ABCD Perimeter is;
2(2x+y)
= 2(2*2.16642012017+4.61590986295)
= 2(8.94875010329)
= 17.8975002066 units.
