Pythagoras theorem is applicable in right-angled triangles only. The measure of line Bd is 6√2 units.
What is Pythagoras theorem?
According to the Pythagoras theorem, the sum of the square of the base and the perpendicular of the right-angled triangle is equal to the hypotenuse of the right-angled triangle.
In ΔABC,
Hypotenuse²= Perpendicular² + Base²
[tex]AC^2= AB^2 + BC^2\\[/tex]
Ac can be written as the sum of AD and DC, therefore,
[tex](AD+DC)^2= AB^2 + BC^2\\\\(6+12)^2= AB^2 + BC^2\\\\18^2 = AB^2+BC^2[/tex]
Let 18²=AB²+BC² be equation1.
In ΔADB,
Hypotenuse²= Perpendicular² + Base²
[tex]AB^2= BD^2 + AD^2\\\\AB^2= BD^2 + 6^2\\\\[/tex]
In ΔBDC,
Hypotenuse²= Perpendicular² + Base²
[tex]BC^2= BD^2 + DC^2\\\\BC^2= BD^2 + 12^2\\\\[/tex]
Substitute the value of AB² and BC² in equation1, we will get,
[tex]18^2 = AB^2+BC^2\\\\18^2 = (BD^2 + 6^2)+(BD^2 + 12^2)\\\\18^2 = BD^2 + 6^2 + BD^2 + 12^2\\\\324-144-36=2BD^2\\\\144=2BD^2\\\\72 = BD^2\\\\BD=6\sqrt2[/tex]
Hence, the measure of line Bd is 6√2 units.
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