Answer:
In ΔABC and Δ DEC:
∠ABC = ∠DEC (both angles are 90 degrees )
We can see that the angles, ∠ABC and ∠DEC are corresponding angles
Since the corresponding angles are equal, we can say that: AB || DE
In ΔABC and Δ DEC:
∠ABC = ∠DEC (Both are 90 degrees)
∠ACB = ∠ECD (Common angle)
Hence, by the AA criterion, we can say that ΔABC ≈ Δ DEC
Finding the Ratio of Similarity:
From the triangle, we see that:
BC = 12 units
EC = 7 units
Since the triangles are similar, they have a constant ratio between their sides
Ratio of sides of ΔABC and Δ DEC = BC / EC
Ratio = 12 / 7
Finding h:
We can see that the sides AB and DE are similar, we also know the ratio of similarity between the sides
We can say that:
h * ratio of similarity = AB
h * 12/7 = 9
h = 63 / 12
h = 5.25 units