in ∆abc b=90° ad=6 ab=12 ac=18 find AE
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Answer:
2√5 cm
Step-by-step explanation:
In ∆ADE and ∆ABC
angle DEA = angle ABC (each 90°)
angle A = angle A (common angle)
∆ADE ~ ∆ABC (AA test of similarity)
6/18 = DE/12
DE = 12×6/18
DE = 4cm
AD² = AE² + DE²
6² = AE² + 4²
36 = AE² + 16
36-16 = AE²
20 = AE²
therefore, AE = 2√5 cm
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