Each equal side of an isosceles triangle is 3 1/2 inches longer than the base. The perimeter of the triangle is 2 feet. Find the length of its base.
base --- x inches
each of equal sides ---- x + 3.5
solve for x
x + 2(x+3.5) = 24
Let's assume the length of the base of the isosceles triangle is x inches.
According to the given information, each equal side of the triangle is 3 1/2 inches longer than the base. So, the length of each equal side is (x + 3 1/2) inches.
The perimeter of the triangle is 2 feet, which is equal to 2 * 12 = 24 inches.
The perimeter of the triangle is calculated by adding the length of all three sides, so we can write the equation:
x + (x + 3 1/2) + (x + 3 1/2) = 24
Let's simplify the equation:
3x + 7 = 24
Subtracting 7 from both sides of the equation:
3x = 24 - 7
3x = 17
Now, isolate x by dividing both sides of the equation by 3:
x = 17/3
To convert the value of x to a mixed number, we divide the numerator (17) by the denominator (3):
17 รท 3 = 5 remainder 2
So, the length of the base, x, is equal to 5 2/3 inches.
To find the length of the base of the isosceles triangle, we can follow these steps:
1. Let's assume the length of the base as "x" inches.
2. Since each equal side of the triangle is 3 1/2 inches longer than the base, the length of each equal side is x + 3 1/2 inches.
3. The perimeter of a triangle is the sum of the lengths of all its sides.
In this case, the perimeter is given as 2 feet, which is equal to 24 inches (since 1 foot = 12 inches).
4. The perimeter of the triangle is the sum of the lengths of the base and the two equal sides. So we can set up the equation:
Perimeter = Base + Equal Side + Equal Side
24 inches = x inches + (x + 3 1/2) inches + (x + 3 1/2) inches
5. Simplifying the equation, we have:
24 inches = 3x + 7 inches
6. Subtracting 7 inches from both sides of the equation, we get:
24 inches - 7 inches = 3x
17 inches = 3x
7. Dividing both sides of the equation by 3, we find:
x = 17 inches / 3
x = 5 2/3 inches
Therefore, the length of the base of the isosceles triangle is 5 2/3 inches.