In Triangle ABC, where PQ||BC,AQ=3,PB=4,AQ=36 then find the value of AC
To find the value of AC, we can use the concept of similar triangles.
First, let's label the given information in the triangle:
Triangle ABC, where PQ || BC
AQ = 3
PB = 4
AQ = 36
Since PQ || BC, we can apply the property of corresponding angles:
∠AQP = ∠ABC (corresponding angles)
∠AQD = ∠ACB (corresponding angles)
Now, let's set up a proportion using the sides of the triangles:
AC / AB = AQ / AD
Since AQ = 3 and AD can be considered 1 (by assuming the same scale), we have:
AC / AB = 3 / 1
Now, let's find the value of AB using similar triangles:
Since PB and BC are parallel lines, we can apply the property of corresponding angles again:
∠PBA = ∠BCA (corresponding angles)
∠PBQ = ∠BAC (corresponding angles)
Using these angles, we can set up another proportion:
AB / PB = AC / PQ
Since AB can be considered 1 (by assuming the same scale), we have:
1 / 4 = AC / PQ
Now, let's substitute the values we know into these proportions:
AC / 1 = 3 / 1
AC = 3
1 / 4 = 3 / PQ
To find the value of PQ, we can cross-multiply:
3 * 4 = 1 * PQ
12 = PQ
Therefore, the value of AC is 3.