Questions: Get ready for congruence, similarity, and triangle trigonom Find the value of x in the isosceles triangle s below. Choose 1 answer: (A) x=13 B x=√44 (c) x=22

Get ready for congruence, similarity, and triangle trigonom

Find the value of x in the isosceles triangle s below.

Choose 1 answer:
(A) x=13

B x=√44
(c) x=22

Transcript text: Get ready for congruence, similarity, and triangle trigonom Find the value of $x$ in the isosceles triangle $s$ below. Choose 1 answer: (A) $x=13$ B $x=\sqrt{44}$ (c) $x=22$

Solution

Solution Steps

Step 1: Identify the properties of the isosceles triangle

In an isosceles triangle, two sides are equal in length. Here, the two equal sides are denoted by $ x $, and the base is 10 units.

Step 2: Apply the Pythagorean theorem

Since the triangle is isosceles, we can draw an altitude from the vertex opposite the base to the midpoint of the base, creating two right triangles. Each right triangle will have legs of lengths 12 (altitude) and 5 (half of the base), and the hypotenuse will be $ x $.

Step 3: Set up the Pythagorean theorem

For one of the right triangles: \[ x^2 = 12^2 + 5^2 \]

Step 4: Calculate the squares

\[ 12^2 = 144 \] \[ 5^2 = 25 \]

Step 5: Sum the squares

\[ x^2 = 144 + 25 \] \[ x^2 = 169 \]

Step 6: Solve for $ x $

\[ x = \sqrt{169} \] \[ x = 13 \]