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?
base of triangle --- x inches
side of triangle ---- 4x inches
4x + 4x + x = 16
9x = 16
x = 16/9
the base is 16/9 inches long
base = 16/9
each side = 64/9
check: 16/9+64/9+64/9
= 144/9 = 16
Why did the isosceles triangle get a restraining order? Because it had a leg problem! Now, back to your question. Let's call the length of one of the legs "x". Since the base length is one fourth the length of one of the legs, we can say the base length is (1/4)x. The perimeter of the triangle is given as 16 inches, so we can set up the equation: x + x + (1/4)x = 16. Simplifying it, we get 5/4x = 16. Solving for x, we find x = (16 * 4) / 5 = 12.8 inches. Therefore, the length of the base is (1/4) * 12.8 = 3.2 inches.
Let's assume the length of each leg of the isosceles triangle is "x" inches.
According to the given information, the length of the base is one fourth the length of one of its legs. Therefore, the length of the base is (1/4)x inches.
The perimeter of a triangle is the sum of the lengths of all its sides.
In this case, the perimeter of the triangle is given as 16 inches.
The perimeter of the triangle is calculated as:
Perimeter = Length of first leg + Length of second leg + Length of base
Given that the length of each leg is "x" inches, and the length of the base is (1/4)x inches, we can write:
16 inches = x inches + x inches + (1/4)x inches
To simplify the equation, we can find a common denominator for x and (1/4)x, which is 4x. This gives us:
16 inches = 4x + 4x + x/4
Combining the like terms, we get:
16 inches = 8x + x/4
To solve the equation, we can multiply both sides by 4 to remove the fraction:
16 inches * 4 = (8x + x/4) * 4
Simplifying further:
64 inches = 32x + x
Combining like terms once again:
64 inches = 33x
To isolate x, we can divide both sides by 33:
64 inches / 33 = x
Simplifying:
x ≈ 1.9394 inches
So, each leg of the triangle is approximately 1.9394 inches long.
Now, we can find the length of the base, which is one fourth of the length of each leg:
Length of the base = (1/4) * x
Length of the base = (1/4) * 1.9394 inches
Calculating:
Length of the base ≈ 0.4848 inches
Therefore, the length of the base of the isosceles triangle is approximately 0.4848 inches.
To solve this problem, we can set up an equation based on the information given. Let's denote the length of one of the legs as 'x'. According to the problem, the length of the base is one fourth the length of one of the legs, so it would be 'x/4'.
The perimeter of an isosceles triangle is the sum of all its sides. In this case, it would be the length of the two legs plus the length of the base, which can be expressed as:
Perimeter = x + x + x/4
We know that the perimeter is given as 16 inches, so we can set up the equation:
16 = x + x + x/4
Now we can solve for 'x':
Multiplying through the equation by 4 to eliminate the fraction:
16 * 4 = 4x + 4x + 1x
64 = 9x
Dividing both sides of the equation by 9:
x = 64/9
Therefore, the length of one of the legs is 64/9 inches.
To find the length of the base, we substitute this value back into our equation for the base:
Base = x/4 = (64/9) / 4 = 64/36 = 16/9 inches
So, the length of the base of the isosceles triangle is 16/9 inches.