Answer:
The value of x is 15 cm.
Step-by-step explanation:
There are two triangles in the diagram that share a common side.
The triangles are:
ABC and BDC
First we have to find the third side of BDC so that we can use it to find the value of x.
The triangle is a right angled triangle so Pythagoras theorem can be used to find the third side.
In the triangle
[tex]Base = BD =10cm\\Hypotenuse = BC = ?\\Perpendicular = CD = 2\sqrt{11}cm[/tex]
Pythagoras theorem is given as:
[tex](Hypotenuse)^2 = (Base)^2 + (Perpendicular)^2\\BC^2 = BD^2 + CD^2\\BC^2 = (10)^2 + (2\sqrt{11})^2\\BC^2 = 100+(2^2 * 11)\\BC^2 = 100+(4*11)\\BC^2 = 100+44\\BC^2 = 144\\\sqrt{BC^2} = \sqrt{144}\\BC = 12cm[/tex]
Now for triangle ABC
[tex]Base = BC = 12 cm\\Perpendicular = AB = 9 cm\\Hypotenuse = AC = x\\[/tex]
Using Pythagoras theorem
[tex]AC^2 = BC^2+AB^2\\x^2 = (12)^2 + (9)^2\\x^2 = 144+81\\x^2 = 225\\\sqrt{x^2} = \sqrt{225}\\x = 15cm[/tex]
Hence,
The value of x is 15 cm.
