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Ymorist [56]
2 years ago
6

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

Mathematics
1 answer:
Alinara [238K]2 years ago
8 0

Answer:

x=15 cm

Step-by-step explanation:

The two triangles in the diagram are:

ABC and BDC

First we have to find the third side (hypotenuse) of BDC so that we can use it to find the value of x.

Hypotenuse is the largest side of a triangle which is usually in front of the right angle.

So in BDC

Base = BD =10cm\\Hypotenuse = BC = ?\\Perpendicular = CD = 2\sqrt{11}cm

Applying Pythagoras theorem:

(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

Solving for triangle ABC

Base = BC = 12 cm\\Perpendicular = AB = 9 cm\\Hypotenuse = AC = x\\

Applying Pythagoras theorem

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

Hence,

x=15 cm

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