Question

Find the value of x in the isosceles triangle shown below

Answer 1

Answer:

The answer is 12

Hope it helps

Answer 2

Answer:

x = 12

Step-by-step 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 $\frac{1}{2}$ x , hypotenuse $\sqrt{45}$ , then

($\frac{1}{2}$ x )² + 3² = ($\sqrt{45}$ )²

$\frac{1}{4}$ x² + 9 = 45 ( subtract 9 from both sides ²)

$\frac{1}{4}$ x² = 36 ( multiply both sides by 4 to clear the fraction )

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

x = $\sqrt{144}$ = 12