The third side of an isosceles right triangle can never be an integer. Since an integer is a special form of a ration number where the denominator is equal to 1, this means that sqrt(2) * a can never be an integer. The square root of 2 is an irrational number, so sqrt(2) * a can never be a rational number. Since sqrt(a^2) is equal to a, the formula becomes: Since sqrt(2 * a^2) is equivalent to sqrt(2) * sqrt(a^2), then the equation becomes: Take the square root of both sides of the equation of c^2 = 2 * a^2 and you will get: You want to solve for c which is the length of the hypotenuse. The formuls of c^2 = a^2 + b^2 becomes c^2 = a^2 + a^2 which becomes c^2 = 2 * a^2. This means that x = b, so you can replace b in the formula with a because b is the same length as a. Since the triangle is an isosceles right triangle, then the legs are equal to each other. The formula to find the length of the hypotenuse of a right triangle is:Ī and b are the legs of the right triangole. The side of the triangle that is not one of the equal sides of the triangle is the hypotenuse of this right triangle. The vertex angle has to be 90 degrees for the right triangle to be an isosceles right triangle. If it's an isosceles right triangle then the hypotenuse of the right triangle is the base of the triangle. The third angle of the triangle is the vertex of the triangle which is the angle between the two equal sides.īUT YOU SAID AN ISOSCELES "RIGHT" TRIANGLE.ĬONTINUE READING TO SEE WHY THE THIRD SIDE CANNOT BE AN INTEGER WHEN THE ISO9SCELES TRIANGLE IS A RIGHT TRIANGLE. Since it is an isosceles triangle, then two sides are equal and the two base angles are equal. The base angles of the isosceles triangle will be different, depending on the length of the third side. There are 13 integers between 0 and 14 and not including 0 and 14. That means the third side can be any number between 0 and 14, but not including 0 or 14.
Since the difference between the two sides of 7 each is 0, this means that the third side has to have a length greater than 0. The other restriction is that the length of the third side is greater than the difference between the lengths of the other two sides. So our only restriction, if two of the sides are 7, is that the third side has to be less than 14.
If it was, then that would violate one of the properties of a triangle that the sum of the lengths of any two sides of the triangle must be greater than the length of the third side. We can make the third side any length we want as long as the third side is not greater than or equal to 14. We'll now construct a triangle with two sides of equal length of 7. The only requirements is that two of the sides have the same length. You can put this solution on YOUR website!Īn isosceles triangle can have sides that are integers.Ĭan it have all 3 sides of integer length.
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