If two sides of an isosceles triangle are 3cm and 8cm what is the length of the third side

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Isosceles triangle calculator is the best choice if you are looking for a quick solution to your geometry problems. Find out the isosceles triangle area, its perimeter, inradius, circumradius, heights and angles - all in one place. If you want to build a kennel, find out the area of Greek temple isosceles pediment or simply do your maths homework, this tool is here for you. Experiment with the calculator or keep reading to find out more about the isosceles triangle formulas.

An isosceles triangle is a triangle with two sides of equal length, which are called legs. The third side of the triangle is called base. Vertex angle is the angle between the legs and the angles with the base as one of their sides are called the base angles.

Properties of the isosceles triangle:

• it has an axis of symmetry along its vertex height
• two angles opposite to the legs are equal in length
• the isosceles triangle can be acute, right or obtuse, but it depends only on the vertex angle (base angles are always acute)

The equilateral triangle is a special case of a isosceles triangle.

To calculate the isosceles triangle area, you can use many different formulas. The most popular ones are the equations:

1. Given arm a and base b:

   area = (1/4) * b * √( 4 * a² - b² )

2. Given h height from apex and base b or h2 height from other two vertices and arm a:

   area = 0.5 * h * b = 0.5 * h2 * a

3. Given any angle and arm or base

area = (1/2) * a * b * sin(base_angle) = (1/2) * a² * sin(vertex_angle)

Also, you can check our triangle area calculator to find out other equations, which work for every type of the triangle, not only for the isosceles one.

To calculate the isosceles triangle perimeter, simply add all the triangle sides:
perimeter = a + a + b = 2 * a + b

Isosceles triangle theorem, also known as the base angles theorem, claims that if two sides of a triangle are congruent, then the angles opposite to these sides are congruent.

Also, the converse theorem exists, stating that if two angles of a triangle are congruent, then the sides opposite those angles are congruent.

A golden triangle, which is also called sublime triangle is an isosceles triangle in which the leg is in the golden ratio to the base:

a / b = φ ~ 1.618

The golden triangle has some unusual properties:

• It's the only triangle with three angles in 2:2:1 proportions
• It's the shape of the triangles found in the points of pentagrams
• It's used to form a logarithmic spiral

Let's find out how to use this tool on a simple example. Have a look at this step-by-step solution:

1. Determine what is your first given value. Assume we want to check the properties of the golden triangle. Type 1.681 inches into leg box.
2. Enter second known parameter. For example, take a base equal to 1 in.
3. All the other parameters are calculated in the blink of an eye! We checked for instance that isosceles triangle perimeter is 4.236 in and that the angles in the golden triangle are equal to 72° and 36° - the ratio is equal to 2:2:1, indeed.

You can use this calculator to determine different parameters than in the example, but remember that there are in general two distinct isosceles triangles with given area and other parameter, e.g. leg length. Our calculator will show one possible solution.

If 3cm is the waist length, 8cm is the bottom length, ∵ 3 + 3 = 6 ＜ 8, it can't form a triangle, ∵ which is not suitable for the problem, and it is omitted; if 3cm is the bottom length, 8cm is the waist length, then the circumference of the triangle is: 3 + 8 + 8 = 19 (CM). So the answer is: 19cm

It is known that the circumference of an isosceles triangle is 29 cm and one side is 5 cm

1. If 5cm is waist length, the third side length is 29-5-5 = 9cm 2. If 5cm is not waist length, waist length is (29-5) / 2 = 12cm

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Triangle Properties:The sum of the length of two sides of a triangle is greater than the length of the third side.In the same way, the difference between the length of two sides should be less than the length of the third side.Now, from the given question we have the two sides of the isosceles triangle as 3 cm, 8 cmNow, here as the triangle is isosceles so the third side should be equal to any of the given two sides.Now, let us assume that the third side as 3 cm the we have\[3+3<8\]Here, it does not satisfy the property of the triangle and if any one of the three possibilities does not satisfy the property of the triangle it cannot form a triangle.Thus, the third side cannot be 3 cmNow, if we consider the third side as 8 cm then we get,\[3+8>8\]Here, it satisfies the property of triangle Thus, the third side is 8 cmHence, the correct option is (b).Note:Instead of using the property that the sum of length of two sides of a triangle is greater than the third side we can also use that the difference of length of two sides of a triangle is less than the third side. Both the methods give the same result.It is important to note that here we cannot use any sine rule or cosine rule of the triangle as we don't know the angles and we don't have specific sides. So, it is suggested to just check the property of triangle first and then think of other higher methods.

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