Question

Special right triangles

Answer 1

The exact value of x is
`6√(2)`

The approximated value of x is 8.49

Explanation:

Let us revise the rules in the right angle triangle when we draw the perpendicular from the right angle to the hypotenuse

In triangle ABC

• Angle B is a right angle
• The hypotenuse is AC
• BD ⊥ AC

1. (AB)² = AD × AC

2. (BC)² = CD × AC

3. (BD)² = AD × CD

4. BD × AC = AB × BC

From the given figure

x represents the length of the ⊥ line from the right angle to the hypotenuse

To find x let us use rule number 3

∵ (BD)² = (AD) × (CD)

∵ BD = x , AD = 3 , CD = 24

∵ x² = 3 × 24

∴ x² = 72

- Use √ for both sides

∴ x =
`6√(2)`

- Find its value by decimal

∴ x = 8.485281374

- Round it to the nearest hundredth

∴ x ≅ 8.49