In the given figure, altitude BD is drawn to the hypotenuse AC of a right triangle ABC. The length of different line segments are marked. Find x and y.
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Answer:
x = 6
y = 2√5
Step-by-step explanation:
AC = AD + CD = 4 + 5 = 9
AC² = AB² + BC²
=> 9² = x² + BC²
=> BC² = 81 - x²
Also BC² = 5² + y²
=> BC² = 25 + y²
81 - x² = 25 + y²
=> x² + y² = 56
also x² = 4² + y²
=> x² = 16 + y²
=> 16 + y² + y² = 56
=> 2y² = 40
=> y² = 20
=> y = 2√5
x² = 16 + y²
=> x² = 16 + 20
=> x² = 36
=> x = 6
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Another Way to solve
in Δ ADB & Δ ABC
∠A - common
∠D = ∠B
=> Δ ADB ≈ Δ ABC
=> AD/AB = AB/AC
=> 4/x = x/9
=> x² = 36
=> x = 6
y² = 6² - 4²
=> y = 2√5
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