an isosceles triangle is one in which two sides are the same length. The perimeter of an isosceles triangle is 36cm if the length of the congruent sides is 4 times the length of the third side, find the dimentions of the triangle

if b is base

8 b + b = 36
9 b = 36
b = 4
then 4 b = 16
so 16 , 16 and 4

To find the dimensions of the isosceles triangle, we can set up an equation based on the information given.

Let's assume that the length of the congruent sides is "x," and the length of the third side is "y."

According to the problem, the perimeter of the triangle is 36 cm. So, we can write the equation:

x + x + y = 36

Since the length of the congruent sides is 4 times the length of the third side, we can also write:

x = 4y

Now, we can substitute the value of "x" from the second equation into the first equation:

4y + 4y + y = 36

Combine like terms:

9y = 36

Divide both sides by 9:

y = 4

Now, we can find the value of "x" by substituting the value of "y" into the second equation:

x = 4y = 4(4) = 16

So, the dimensions of the isosceles triangle are:

Length of the congruent sides: 16 cm
Length of the third side: 4 cm