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प्रश्न
ABC is a right angled triangle with ∠ABC = 90°. D is any point on AB and DE is perpendicular to AC. Prove that :
If AC = 13 cm, BC = 5 cm and AE = 4 cm. Find DE and AD.
उत्तर
Since ΔADE ~ ΔACB, their sides are proportional
`=> (AE)/(AB) = (AD)/(AC) = (DE)/(BC)` ....(1)
In ΔABC, by Pythagoras Theorem, we have
`AB^2 + BC^2 = AC^2`
`=> AB^2 + 5^2 = 13^2`
`=> AB = 12 cm`
From equation 1 we have
`4/12 = (AD)/13 = (DE)/5`
`=> 52/12= (AD)`
`=> AD = 4 1/3cm`
Also `4/12 = (DE)/5`
`=> DE = 20/12 = 5/3 = 1 2/3 cm`
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