Question

Find the value of x in the isosceles triangle shown below

Answer 1

x = 12

Explanation:

Since the 2 legs and base angles are congruent the triangle is isosceles.

The line from the vertex to the base is a perpendicular bisector dividing the triangle into 2 right triangles.

Using Pythagoras' identity in either of the 2 right triangles with legs 3 and
`(1)/(2)` x , hypotenuse
`√(45)` , then

(
`(1)/(2)` x )² + 3² = (
`√(45)` )²

`(1)/(4)` x² + 9 = 45 ( subtract 9 from both sides ²)

`(1)/(4)` x² = 36 ( multiply both sides by 4 to clear the fraction )

x² = 144 ( take the square root of both sides )

x =
`√(144)` = 12

Answer 2

The answer is 12

Hope it helps