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Chapter 8: Q20. (page 292)

find the value of x.

Short Answer

Expert verified

The value of x is 8.

Step by step solution

01

Step 1. Given information.    

The two sides of triangle are same that is 10 and third side is 12.

02

Step 2. Concept used.

  1. In isosceles triangle, the vertex angle bisector of isosceles triangle is perpendicular bisector of the base.
  2. Pythagoras Theorem state that in a right angle triangle, the square of the hypotenuse is equal to the sum of squares of other sides.
03

Step 3. Now find the value.

BC=CD(byconcept1)BD=12BC+CD=122BC=12BC=6

Now we can use Pythagoras theorem in 螖ABC.

x2+62=102x2+36=100x2=64

Taking square root we get.

x=卤64x=卤8

Since, distance is always a positive quantity so we neglect negative sign.

Therefore, the value of x is 8.

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