The length of the base of an isosceles triangle is one fourth the length of one of its legs. If the perimeter of the triangle is 16 inches, what is the length of the base?
Let x = leg length, then 1/4x = base length.
1/4x + x + x = 16
Solve for x, and divide by 4.
37/16
To solve this problem, we can break it down into a few steps:
Step 1: Let's denote the length of one of the legs of the isosceles triangle as 'x'. Since the length of the base is one-fourth the length of one of its legs, the length of the base can be represented as 'x/4'.
Step 2: The perimeter of a triangle is the sum of the lengths of all its sides. For this isosceles triangle, it consists of two equal legs and the base. Therefore, the perimeter is given by the equation:
perimeter = leg + leg + base
Step 3: We are given that the perimeter of the triangle is 16 inches, so we can substitute '16' for 'perimeter' in the equation from Step 2:
16 = x + x + x/4
Step 4: Simplify the equation from Step 3 to solve for 'x':
16 = 2x + x/4
Step 5: To eliminate the fraction, we can multiply the entire equation by 4:
64 = 8x + x
Step 6: Combine like terms on the right side of the equation:
64 = 9x
Step 7: Solve for 'x' by dividing both sides of the equation by 9:
x = 64/9
Therefore, the length of one of the legs, 'x', is approximately 7.11 inches.
Step 8: Finally, we can find the length of the base by substituting the value of 'x' into our original equation:
base = x/4
Substituting the value of 'x' we found in Step 7:
base = (64/9)/4
Simplifying, we get:
base = 16/9
Therefore, the length of the base of the isosceles triangle is approximately 1.78 inches.