An isosceles triangle has a perimeter of 30cm

Hint: Determine the sides of the triangle first. And then use Heron’s formula for the area of a triangle. According to the question, the perimeter of the triangle is $30cm$. Then the semi-perimeter will be: $ \Rightarrow s = \dfrac \times b \times h$. We’ll get the same result.

Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

A n isosceles triangle is said to have two equal sides and two equal internal angles. The perimeter of an isosceles can be found if the base and sides are known. Formula of Isosceles Triangle Perimeter \[\large Perimeter\;of\;Isosceles\;Triangle,P=2\,a+b\] Where, a = length of the two equal sides b = Base of the isosceles triangle Solved Example Question 1: What is the perimeter of an isosceles triangle when a = 9 cm and b = 6 cm? Solution: Given, a = 9 cm b = 6 cm Perimeter of an isosceles triangle = 2a + b = 2(9) + 6 = 18 + 6 cm = 24 cm

Hint: An isosceles triangle is a triangle with two of its sides equal. Relate the length of the base to the congruent sides. Then solve for the sides using the perimeter of the triangle. Complete step-by-step answer: An isosceles triangle is a triangle that has two sides of equal length. The two corresponding angles of the isosceles triangle are also equal. Let the length of the equal sides be x and the length of the other side be y. It is given that the length of the base is 3 cm shorter than the length of the congruent sides. Hence, we have the following: \[y = x - 3..........(1)\] The perimeter of a figure is defined as the length of the path that surrounds an area. For a polygon, it is the sum of its sides. The perimeter of a triangle is the sum of all the three sides. The perimeter is given to be 30 cm, hence, we have: \[x + x + y = 30...........(2)\] Substituting equation (2) in equation (1), we have: \[x + x + x - 3 = 30\] Simplifying the equation, we have: \[3x - 3 = 30\] Solving for x, we have: \[3x = 30 + 3\] \[3x = 33\] \[x = \dfrac\] \[x = 11cm\] Hence, the values of the equal sides are 11 cm each. Substituting x in equation (1), we have: \[y = 11 - 3\] \[y = 8cm\] Hence, the lengths of the sides are 11 cm, 11 cm, and 8 cm. Note: Do not conclude after finding the length of the equal sides. You are asked to find the length of all three sides. Hence, you need to find both the length of equal sides and the base.

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