The other dimensions of the triangle, such as its height, area, and perimeter, can be calculated by simple formulas from the lengths of the legs and base.Įvery isosceles triangle has an axis of symmetry along the perpendicular bisector of its base. The two equal sides are called the legs and the third side is called the base of the triangle. Isosceles triangles have been used as decoration from even earlier times, and appear frequently in architecture and design, for instance in the pediments and gables of buildings. The mathematical study of isosceles triangles dates back to ancient Egyptian mathematics and Babylonian mathematics. Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal length, the latter version thus including the equilateral triangle as a special case.Įxamples of isosceles triangles include the isosceles right triangle, the golden triangle, and the faces of bipyramids and certain Catalan solids. In geometry, an isosceles triangle ( / aɪ ˈ s ɒ s ə l iː z/) is a triangle that has two sides of equal length. Replace c by a question mark (?) and say to yourself the following: 18 + ? = 30 or what can I add to 18 to get 30 ? 18 + 12 = 30, so c = 12 Example #11 If P = 20 cm, b = 7 and c = 8, what is a? Using the formula P = a + b + c, replace everything you know or everything given to you into the formula.Isosceles triangle with vertical axis of symmetry However, some mental math should provide you with an answer too. Things that are given are P = 30, a = 8, and b = 10 Replacing them into the formula gives: 30 = 8 + 10 + c 30 = 18 + c You end up with an addition equation that you can solve to get c. If P = 30 cm and a = 5 and b = 7, what is c? Using the formula P = a + b + c, replace everything you know or everything given to you into the formula. How to find the length of a side of the triangle when the perimeter and two sides are given Once you find the third side, add the three sides to find the perimeter of the triangle. Since you already know two sides of the triangle, all you need to do is to use the Law of Cosines to find the third side. In this case, you need to look for the length of the hypotenuse before looking for the perimeter.Ī triangle when two sides and the angle between these two sides are known is an SAS triangle or a side-angle-side triangle. Suppose the lengths of the legs of a right-angled triangle are known, but the length of the hypotenuse is not known. P = 3 + 2 = 5 cm Perimeter of a right triangle using the Pythagorean theorem P = 2 × a + b = 2 × 10 + 15įind the perimeter of an isosceles triangle if the length of the two equal sides is 1.5 cm and the length of the third side is 2 cm. Examples showing how to find the perimeter of an isosceles triangleįind the perimeter of an isosceles triangle if the length of the two equal sides is 10 inches and the length of the third side is 15 inches. Therefore, the formula to use to find the perimeter of an isosceles triangle is P = 2 × a + b. Here is how to find the perimeter (P) or distance around the outside of an isosceles triangle.
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