In an isosceles triangle, if the equal sides are each 10 cm and the base is 12 c

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Question: In an isosceles triangle, if the equal sides are each 10 cm and the base is 12 cm, what is the height of the triangle?

Options:

Correct Answer: 6 cm

Solution:

Using the Pythagorean theorem, the height can be found by splitting the triangle in half: height = √(10^2 - 6^2) = √(100 - 36) = √64 = 8 cm.

In an isosceles triangle, if the equal sides are each 10 cm and the base is 12 cm, what is the height of the triangle?

In an isosceles triangle, if the equal sides are each 10 cm and the base is 12 cm, what is the height of the triangle?

Step 1: Identify the triangle as isosceles, with two equal sides of 10 cm and a base of 12 cm.
Step 2: Split the triangle in half vertically to create two right triangles.
Step 3: The base of each right triangle is half of the original base, so it is 12 cm / 2 = 6 cm.
Step 4: The height of the triangle is the vertical line from the top vertex to the base.
Step 5: Use the Pythagorean theorem, which states that in a right triangle, a^2 + b^2 = c^2, where c is the hypotenuse (10 cm), a is the height, and b is half the base (6 cm).
Step 6: Set up the equation: height^2 + 6^2 = 10^2.
Step 7: Calculate 6^2 = 36 and 10^2 = 100.
Step 8: Substitute these values into the equation: height^2 + 36 = 100.
Step 9: Solve for height^2 by subtracting 36 from both sides: height^2 = 100 - 36.
Step 10: Calculate 100 - 36 = 64.
Step 11: Find the height by taking the square root of 64: height = √64 = 8 cm.

Isosceles Triangle Properties – Understanding the properties of isosceles triangles, including how to find the height by using the Pythagorean theorem.
Pythagorean Theorem – Application of the Pythagorean theorem to find the height of a triangle when given the lengths of the sides.
Triangle Segmentation – The method of splitting the triangle into two right triangles to simplify calculations.