Let P = area of triangle ABC Q = area of triangle ACD
The two areas mentioned above are in ratio 1.5:1 which basically means P = 1.5*k Q = 1*k for some value k Notice how P/Q = (1.5k)/(1k) = 1.5 which proves that P:Q = 1.5:1
We can find the value of k by determining the area of triangle ABC P = area of triangle ABC P = (base)*(height)/2 P = 36*10/2 P = 360/2 P = 180
If P = 180, then P = 1.5*k 1.5*k = 180 k = 180/1.5 k = 120
Telling us that Q = 1*k Q = 1*120 Q = 120 Q = area of triangle ACD area of triangle ACD = 120 note how P/Q = 180/120 = 1.5 so P:Q = 1.5:1
We'll use this area to find the base of triangle ACD which is AD
Area of Triangle ACD = (base)*(height)/2 120 = AD*10/2 120*2 = AD*10 240 = AD*10 240/10 = AD 24 = AD AD = 24
