the perimeter of an isosceles triangle is 30 inches. the legs are 1/3 as long as the base. set up an equation to find each side length of the triangle.
Let's denote the length of the base of the isosceles triangle as "b" and the length of each leg as "l". We are given that the perimeter of the triangle is 30 inches.
The perimeter of a triangle is the sum of the lengths of all its sides.
In this case, we can set up the equation as follows:
b + l + l = 30
Since the legs are 1/3 as long as the base, we can substitute the value of the legs in terms of the base:
b + (1/3)b + (1/3)b = 30
Simplifying the equation further:
b + 2/3 * b = 30
Adding the like terms:
3/3 * b + 2/3 * b = 30
Combining the terms on the left side:
5/3 * b = 30
To find the length of the base, we can multiply both sides of the equation by 3/5:
(5/3 * b) * (3/5) = 30 * (3/5)
This simplifies to:
b = (90/5) / (3/5)
Simplifying further:
b = 90/3
b = 30
Now, to find the length of each leg, we can substitute the value of the base back into the equation:
l = (1/3) * 30
Simplifying:
l = 10
Therefore, the base of the isosceles triangle is 30 inches, and each leg is 10 inches.
To find each side length of the triangle, we can set up an equation using the given information. Let's denote the length of the base of the triangle as 'b', and the length of each leg as 'l'.
According to the problem, the perimeter of the triangle is 30 inches. The perimeter of any polygon is the sum of all its side lengths. In this case, the perimeter of the triangle can be expressed as:
perimeter = base + leg + leg = b + l + l = 30
The problem also states that the length of each leg is one-third (1/3) the length of the base. So, we can express this relationship as:
leg = (1/3) * base = (1/3) * b
Now, substitute this expression for 'leg' into the perimeter equation:
b + (1/3) * b + (1/3) * b = 30
Simplifying the equation, we can combine like terms:
b + (2/3) * b = 30
Combining the 'b' terms:
(3/3) * b + (2/3) * b = 30
Now, we can multiply through by 3 to clear the fraction:
3b + 2b = 90
Finally, simplifying the equation:
5b = 90
This gives us the equation to find the length of the base of the triangle.