Mathematics Question and Solution
Let AD = 2AB.
For AB = 2 units, AD = BC = 4 units.
Angle APD is;
= atan(4)°
PD = √(4²+1)
PD = √(17) units.
Considering similar triangles APD and QCD ratios.
1 = a
√(17) = 2
Crossing Multiply.
a = (2/√(17)) units.
a = 0.48507125007 units.
a is DQ.
PQ = √(17)-0.48507125007
PQ = 3.63803437554 units.
Angle BPQ = 180-atan(4)
= 104.03624346793°
Calculating QB.
Notice, BC is 4 units.
(QB)² = 3.63803437554²+1-2*3.63803437554cos104.03624346793
QB = 4 unit.
It implies;
BC = QB Proved.
