Question

question 9
10 pts
g.gsr.6.3 (hc)
find the value of x.
image of an isosceles triangle with two equal sides of length 12, base 14, and a height x drawn from the apex to the base, forming a right angle
accessible description
options:
13
√95
√193
√52

Explanation:

Step1: Analyze the triangle

The triangle is isosceles, and the altitude (x) splits the base into two equal parts. So each part of the base is $\frac{14}{2} = 7$.

Step2: Apply Pythagorean theorem

In the right triangle formed (with hypotenuse 12 and one leg 7), use $a^2 + b^2 = c^2$. Here, $x^2 + 7^2 = 12^2$.

Step3: Solve for x

$x^2 = 12^2 - 7^2 = 144 - 49 = 95$. So $x = \sqrt{95}$.

Answer:

$\sqrt{95}$