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By using Apollonius' theorem, the length of the median of a triangle of sides of length a, b, c is given by:
ma = sqrt( (2b2 + 2c2 - a2) / 4)
where ma is the median that meets the midpoint of a; and similarly for mb and mc. By rearranging this, the sides (a, b, c) of a triangle can be obtained from the lengths of the medians (ma, mb, mc):
a = 2/3 sqrt(2mb2 + 2mc2 - ma2)
b = 2/3 sqrt(2mc2 + 2ma2 - mb2)
c = 2/3 sqrt(2ma2 + 2mb2 - mc2)
Once the sides are known (using the above), the triangle can be drawn fairly easily using a ruler and compasses.
What else can I help you with?
Perimeter of a triangle with base length and height length known?
Is indeterminate.
What is the balance point of a triangle?
The balance point of a triangle, known as the centroid, is the point where the three medians intersect. The centroid divides each median into two segments, with the longer segment being twice the length of the shorter one. This point serves as the center of mass for the triangle, meaning that if the triangle were made of a uniform material, it would balance perfectly at the centroid. The coordinates of the centroid can be calculated by averaging the coordinates of the triangle's vertices.
How do you know when a triangle is 90 degrees?
we know that a triangle is 90 degrees by measuring its length or it can be known as right triangle which measures 90 degrees.
Is 10 a right triangle?
If the length of only one side is known, it is not possible to determine whether or not the triangle is right angled.
What is an ambiguous triangle?
The answer may refer to a triangle for which the length of two sides and the measure of an angle - other than the included angle - are known.
Concurreny of medians of triangle?
The three medians are concurrent at a point known as the triangle's centroid. This is the center of mass of the triangle. Two-thirds of the length of each median is between the vertex and the centroid, while one-third is between the centroid and the midpoint of the opposite side.
Perimeter of a triangle with base length and height length known?
Is indeterminate.
What formula do you use to find the median in an isosceles triangle?
It is not possible to answer the question since it is hopelessly underspecified and does not provide enough information.what information about the triangle is known? All three side lengths, base angle and base side, base angle and leg, apex angle and base, apex angle and leg? These could influence the form of the answer.is the information about the triangle in terms of analytical geometry (coordinates of points and equations of lines) or in some other form?which median? The median from the apex or one of the isosceles medians?what aspect of the median is the formula supposed to give? Its length, equation?
What is the balance point of a triangle?
The balance point of a triangle, known as the centroid, is the point where the three medians intersect. The centroid divides each median into two segments, with the longer segment being twice the length of the shorter one. This point serves as the center of mass for the triangle, meaning that if the triangle were made of a uniform material, it would balance perfectly at the centroid. The coordinates of the centroid can be calculated by averaging the coordinates of the triangle's vertices.
How do you know when a triangle is 90 degrees?
we know that a triangle is 90 degrees by measuring its length or it can be known as right triangle which measures 90 degrees.
Is 5 a right triangle?
If the length of only one side is known, it is not possible to determine whether or not the triangle is right angled.
Is 10 a right triangle?
If the length of only one side is known, it is not possible to determine whether or not the triangle is right angled.
What is an ambiguous triangle?
The answer may refer to a triangle for which the length of two sides and the measure of an angle - other than the included angle - are known.
How would you construct a trapezoid given the length of the top and the bottom and the length of BOTH diagonals?
Consider the trapezium ABCD in which AD and BC are the top and the bottom - parallel and of known length - and AC and BD are the diagonals - also of known length. Suppose AC and BD intersect at O. Then, it can be shown that triangles AOD and COB are similar. Therefore AO/OC = DO/OB = AD/BC where both lengths for the last ratio are known. Then, given AC, it is possible to calculate OC (and AO) and given BD, it is possible to calculate OB (and DO). So all sides of triangle COB are known and so it is easy to construct it. Then simply extend BO to D (adding OD) and CO to A (adding OA). Join BA, AD and DC. Done!
What is a triangle called with only 2sides with the same length?
A triangle with only two sides of the same length is called an isosceles triangle. In an isosceles triangle, the two equal sides are known as the legs, while the third side is called the base. The angles opposite the equal sides are also equal.
What is the length of pr triangle?
The length of a triangle's sides can vary depending on the specific triangle in question. If "pr triangle" refers to a particular triangle defined by specific points or properties, more context is needed to provide an accurate answer. Typically, the lengths of the sides of a triangle can be calculated using the distance formula if the coordinates of the vertices are known. Otherwise, the lengths can be derived from the triangle's dimensions or angles.
What can you say about the sides of a triangle opposite the largest angle?
The side of a triangle opposite the largest angle is the side of greatest length. It is also known as the Hypotenuse.
