Question
The triangle shown is isosceles. Find the length of each side and the perimeter ?
Hint:
A triangle that has 2 sides of equal lengths is known as an isosceles triangle.
The correct answer is: Sides of the given isosceles triangle are 13cm, 13cm & 6 cm and the perimeter is 32cm.
Step-by-step solution:-
From the given diagram, we can observe that-
Sides of the triangle are of lengths '5n - 17' cm, '2n + 1' cm and n cm and sides with lengths (5n - 17) and (2n + 1) are congruent.
Hence, we can conclude that-
5n - 17 = 2n + 1
∴ 5n - 2n = 1 + 17 …................................... (Taking variables and constants on either sides of the equation)
∴ 3n = 18
∴ n = 
........................................ (Dividing both sides by 3)
∴ n = 6 ............................................. (Equation i)
Substituting the value of n in equations of all the sides of the triangle, we get-
Side 1 = a = 5n - 17
∴ Side 1 = a = 5 × 6 - 17 ................................................ (From Equation i)
∴ Side 1 = a = 30 - 17
∴ Side 1 = a = 13 ................................................. (Equation ii)
Side 2 = b = 2n + 1
∴ Side 2 = b = 2 × 6 + 1 ............................................ (From Equation i)
∴ Side 2 = b = 12 + 1
∴ Side 2 = b = 13 ............................................. (Equation iii)
Side 3 = c = n = 6 .......... (From Equation i) .................... (Equation iv)
Perimeter of the given triangle = a + b + c
∴ Perimeter of the given triangle = 13 + 13 + 6 ........................... (From Equations ii, iii & iv)
∴ Perimeter of the given triangle = 32
Final Answer:-
∴ Sides of the given isosceles triangle are 13cm, 13cm & 6 cm and the perimeter is 32cm.
An isosceles triangle is one with two sides of the same length. An isosceles triangle's two opposite angles are equal in size.
¶Triangles are three-sided polygons that are classified into three types based on their sides, such as:
¶Triangle of Scalene (All three sides are unequal)
Triangle of isosceles (Only two sides are equal)
(All three sides are equal) Equilateral triangle
¶Triangle's isosceles perimeter in units of P = 2a + b
¶The area of an isosceles triangle
A = 1/2 x b x h Square units.
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