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
To solve a system of linear equations by graphing, first make sure that you have two linear equations. Then, graph the line represented by each equation and see where the two lines intersect each other. The x and y coordinates of the intersection point will be the solution to the system of equations!
If y is equal to-x + 2 then you can plug that into the second equation as x - 4(-x + 2) = -28 after this distribute out the -4 to get x + 4x - 8 = -28. After this combine the like terms to get 5x = -20. Then get x by itself by dividing by 5 to get x = -4.
