triangle ABC ad is perpendicular BC and. D lies on BC such that 2 DB = 23 CD prove that 5 a b square equal to 5 AC square + bcsquare
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It is not 23 CD it is 2/3 CD
Since ⊿ADB is a right triangle, we have
AB² = AD² + DB².
And since 2DB =3 CD, we know BC = BD + CD BC = 2/3 DB+DB And DB = (3/5) CB.
(1) AB² = AD² + 9/25 BC2.
Similarly ⊿ADC is a right triangle, so
AC² = AD² + DC²,
So Similarly, DC = BC - BDDC= BC (2/5), and
(2) AC² = AD² + (4/25) BC²,
Subtract (1) by (2)
AB² - AC² = (9 - 4)/25 BC² AB² - AC² = 1/5 BC² 5AB² - 5AC² = BC²
So
5 AB² = 5 AC² + BC².
:) Hope this helps!!!!!
Since ⊿ADB is a right triangle, we have
AB² = AD² + DB².
And since 2DB =3 CD, we know BC = BD + CD BC = 2/3 DB+DB And DB = (3/5) CB.
(1) AB² = AD² + 9/25 BC2.
Similarly ⊿ADC is a right triangle, so
AC² = AD² + DC²,
So Similarly, DC = BC - BDDC= BC (2/5), and
(2) AC² = AD² + (4/25) BC²,
Subtract (1) by (2)
AB² - AC² = (9 - 4)/25 BC² AB² - AC² = 1/5 BC² 5AB² - 5AC² = BC²
So
5 AB² = 5 AC² + BC².
:) Hope this helps!!!!!
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