find the value of x of given figure and solve this question step by step plzz help question number D​​

Answer:

15

Step-by-step explanation:

First we need to find the length of BC and for that we gonna use Pysagoras theorem

10^2 + (2√11)^2 = |BC|^2

√144 = |BC|^2

12 = BC Now we will use this to find the value of x

x^2 = 12^2 + 9^2

x^2 = 144 + 81

x^2 = 225

√x^2 = √225

x = 15

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.

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