Question

Please help!! Due soon

Answer 1

Answer: 24 cm

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Explanation:

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