The perimeter of an isosceles triangle is four times the length of the shortest side. The longer sides are 4.5 feet longer than the shortest side. What is the length of each side of the triangle?
y + 2 x = 4 y
x = y + 4.5
so
y + 2(y+4.5) = 4y
3 y + 9 = 4 y
y = 9
x = 13.5
9 + 10 = 21!!!!
bob is a genius!!!
To solve this problem, let's assign variables to the lengths of the sides of the triangle. We'll call the length of the shortest side "x", and since the longer sides are 4.5 feet longer than the shortest side, we can represent their lengths as "x + 4.5".
Now, according to the given information, the perimeter of the triangle is four times the length of the shortest side. The perimeter of a triangle is the sum of all its sides. In this case, we can express the perimeter as:
Perimeter = Shortest side + Longest side + Longest side
Since we know that the perimeter is four times the length of the shortest side, we can write the equation:
4x = x + (x + 4.5) + (x + 4.5)
Simplifying the equation, we have:
4x = x + x + 4.5 + x + 4.5
Combining like terms, we get:
4x = 3x + 9
Now, let's isolate the variable "x". Subtracting 3x from both sides of the equation, we have:
4x - 3x = 3x - 3x + 9
Simplifying further, we get:
x = 9
Therefore, the shortest side of the triangle has a length of 9 feet. To find the lengths of the longer sides, we substitute the value of x back into our expressions for the longer sides:
Longer side = x + 4.5 = 9 + 4.5 = 13.5
Therefore, the lengths of each side of the triangle are: 9 feet, 13.5 feet, and 13.5 feet.