Answer:
12.99
Explanation:
To find the length of the base, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Let's denote the length of the base as "b".
Using the Pythagorean theorem, we have:
b^2 + (15/2)^2 = 15^2
Simplifying the equation:
b^2 + 225/4 = 225
Multiplying both sides of the equation by 4 to eliminate the fraction:
4b^2 + 225 = 900
Subtracting 225 from both sides:
4b^2 = 900 - 225
4b^2 = 675
Dividing both sides by 4:
b^2 = 675/4
Taking the square root of both sides:
b = √(675/4)
Simplifying further:
b = √(675)/√(4)
b = (√(225) * √(3))/2
Since the length of the base cannot be negative, we can disregard the negative square root.
Therefore, the length of the base of the isosceles triangle is (√(225) * √(3))/2, which simplifies to (15 * √(3))/2, or approximately 12.99 cm.