Question

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

Answer 1

Answer:

The correct answer is x = 3√2 units.

Answer 2

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)