Triangle ABC is an equilateral triangle.AD=10 What is the length of CD? Give your answer to the nearest whole number.
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Sra
Do not know where D is. Needs more explanation.
To find the length of CD, we first need to understand the properties of an equilateral triangle. In an equilateral triangle, all three sides are equal in length.
Since triangle ABC is an equilateral triangle and AD = 10, we know that AB, BC, and AC are also each equal to 10.
Let's focus on triangle ADC. Since AC is the base of triangle ADC and CD is the height, we can use the Pythagorean theorem to find the length of CD.
The Pythagorean theorem 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.
In triangle ADC, AC is the hypotenuse, AD is one of the sides, and CD is the other side. So we have:
AC^2 = AD^2 + CD^2
Substituting the known values, we get:
10^2 = 10^2 + CD^2
100 = 100 + CD^2
CD^2 = 100 - 100
CD^2 = 0
From this equation, we can see that CD^2 = 0, which means CD must be 0. Therefore, the length of CD is 0.
Please note that this result may seem counterintuitive, but it is because the given information is not consistent. In an equilateral triangle, all sides should be equal. If AD = 10, then all sides of the triangle should also be 10. However, based on the given information, triangle ADC does not fulfill the conditions of an equilateral triangle.