Question

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

Answer 1

x=15 cm

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√(11)cm`

Applying Pythagoras theorem:

`(Hypotenuse)^2 = (Base)^2 + (Perpendicular)^2\\BC^2 = BD^2 + CD^2\\BC^2 = (10)^2 + (2√(11))^2\\BC^2 = 100+(2^2 * 11)\\BC^2 = 100+(4*11)\\BC^2 = 100+44\\BC^2 = 144\\√(BC^2) = √(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\\√(x^2) = √(225)\\x = 15cm`

Hence,

x=15 cm