A right triangle is shown. An altitude is drawn to form a right angle with the opposite side and split the side into lengths of
3 and 3. What is the value of x? One-third StartRoot 2 EndRoot units One-half StartRoot 3 EndRoot units 2 StartRoot 3 EndRoot units 3 StartRoot 2 EndRoot units
2 answers:
Answer:
x = 3√2 units.
Step-by-step explanation:
Let Δ ABC is a right triangle with ∠ ABC = 90°.
We draw an altitude from B on AC at point D and AD = CD = 3 units.
We have to find x.
Now, BD is the perpendicular bisector of side AC and hence, Δ ABC is a right isosceles triangle.
So, AB = BC = x
And AC = 3 + 3 = 6 units.
So, applying Pythagoras Theorem, AB² + BC² = AC²
⇒ x² + x² = 6²
⇒ 2x² = 36
⇒ x² = 18
⇒ x = 3√2 units. (Answer)
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