The perimeter of an isosceles triangle is at least 56 inches. The base is twice the length of one of the sides of equal measurement of the isosceles triangle. What is the least possible value of the base of the triangle?
2*x + 2x >= 56
solve for 2x
This is either a typo or a trick question
If the equal sides add up to the length of the base, it is not a triangle but a line.
a = 56/4 = 14 minimum
base = 14+14 = 28 at least
because if the perimeter is >56 then the base can be longer.
Let's assume that the length of each equal side of the isosceles triangle is "x" inches.
According to the given information, the perimeter of the triangle is at least 56 inches.
Perimeter of the triangle = sum of all three sides
Therefore, 2x + x + x = 56
Simplifying this equation, we get:
4x = 56
Dividing both sides of the equation by 4, we have:
x = 14
Therefore, the length of each equal side of the isosceles triangle is 14 inches.
Now, we are given that the base of the triangle is twice the length of one of the sides of equal measurement.
So, the length of the base = 2 * 14 inches = 28 inches.
Hence, the least possible value of the base of the triangle is 28 inches.
To find the least possible value of the base of the isosceles triangle, we first need to determine the minimum value of the side of equal measurement. Let's assume the length of one of the sides is "x".
Since the triangle is isosceles, the other side of equal measurement will also be "x".
According to the given information, the perimeter of the triangle is at least 56 inches. The perimeter of a triangle is the sum of all its sides.
In this case, the perimeter is:
x + x + 2x = 4x
Since the perimeter is at least 56 inches, we can write the following inequality:
4x ≥ 56
To find the minimum value of x, we need to solve this inequality. Dividing both sides by 4:
x ≥ 14
So, the minimum value of x (and the side of equal measurement) is 14 inches.
Now, we need to determine the base of the triangle. According to the given information, the base is twice the length of one of the sides.
Therefore, the base = 2x = 2(14) = 28 inches.
Hence, the least possible value of the base of the isosceles triangle is 28 inches.