An isosceles triangle is a type of triangle where 2 sides are equal.
Picture out 2 triangles with the same base length. On the first triangle, its legs are twice the length of the legs of the second triangle.
To put it into variables, let: B = the same base length of the two triangles A = the length of one leg the smaller triangle 2A = the length of one leg of the bigger triangle
Given: Perimeter of smaller triangle = 23cm Perimeter of bigger triangle = 43cm
Recall the formula for solving the perimeter of a triangle: Perimeter = A + B + C
where, A, B, and C are the legs of the triangle
Since the triangle involved is an isosceles triangle, therefore, we can say that Perimeter = 2A + B , 2 legs are equal ( A=C )
Substituting the given perimeter value to the formula.
23cm = 2A + B ⇒ equation 1 (smaller triangle) 43cm = 2(2A) + B ⇒ equation 2 (bigger triangle)
Simplifying equation 2. 43cm = 4A + B (rearranging) B = 43cm - 4A ⇒ equation 3
Substituting equation 3 to equation 1: (equation 1) 23cm = 2A + B 23cm = 2A + (43cm - 4A) 23cm = -2A + 43cm 2A = 43cm - 23cm 2A = 20cm ⇒ length of the leg of the bigger triangle A = 10cm ⇒ length of the leg of the smaller triangle
To solve for the base length, just substitute the value of A to equation 3 (equation 3) B = 43cm - 4A B = 43cm - 4(10cm) B = 3 cm
Final Answer:
• For the smaller triangle, the length of the sides are 10cm, 10cm, and 3cm • For the bigger triangle, the length of the sides are 20cm, 20cm, and 3cm
