Answer:
x ≈ 2.1
y ≈ 5.4
w = 5
Step-by-step explanation:
The given parameters are;
Segment AC = 13
Segment BC = y
Segment AD = 12
Segment CD = w
Segment BD = x
By Pythagoras's theorem, for the right triangle ΔACD, we have;
[tex]\overline {AC}[/tex]² = [tex]\overline {AD}[/tex]² + [tex]\overline {CD}[/tex]²
∴ 13² = 12² + w²
w² = 13² - 12² = 25
w = √(25) = 5
w = 5
By, Pythagoras's theorem similarly, in the right triangle ΔBCD we have;
y² = x² + w²
∴ y² = x² + 5² = x² + 25
y² = x² + 25
In the right triangle ΔABC we have;
[tex]\overline {AB}[/tex]² = [tex]\overline {AC}[/tex]² + [tex]\overline {CB}[/tex]²
∴ (12 + x)² = 13² + y² = 13² + (x² + 25)
(12 + x)² = 13² + (x² + 25)
144 + 24·x + x² = 13² + x² + 25
24·x = 13² + 25 - 144 = 50
x = 50/24 ≈ 2.1
x ≈ 2.1
y² = x² + 25
∴ y = √(x² + 25) = √((50/24)² + 25) = 65/12 ≈ 5.4
y ≈ 5.4
