Isosceles triangle base is 7 more than one-half times the legs. Perimeter is 22 centimeter Find length of each leg
To find the length of each leg of an isosceles triangle, we'll start by setting up an equation based on the given information.
Let's denote the length of each leg as 'x'.
According to the given information, the base of the isosceles triangle is 7 more than one-half times the legs. So, the length of the base can be expressed as:
Base = (1/2)x + 7
Since the triangle is isosceles, the lengths of the legs are equal. Hence, we can express the perimeter of the triangle using the length of the legs as:
Perimeter = 2 * Leg + Base
Given that the perimeter is 22 centimeters, we can substitute the values into the equation and solve for 'x':
22 = 2 * x + (1/2)x + 7
Combining like terms:
22 = (5/2)x + 7
Subtracting 7 from both sides:
22 - 7 = (5/2)x
15 = (5/2)x
To solve for 'x', we multiply both sides of the equation by 2/5:
15 * (2/5) = (5/2)x * (2/5)
6 = x
So, the length of each leg of the isosceles triangle is 6 centimeters.