the perimeter of an isosceles triangle is 73 cm. the base measures 3 cm more than one half the measure of a leg. what is the measure of each side of the triangle
let each leg's length be x cm
so the base is (1/2)x + 3
so ....
x + x + x/2 + 3 = 73
2x + x/2 = 70
my suggestion: multiply each term by 2, and it becomes very easy
To find the measure of each side of the isosceles triangle, we can set up an equation using the given information.
Let's denote the measure of each leg as x. Since the base measures 3 cm more than one half the measure of a leg, the length of the base would be (x/2) + 3.
Given that the perimeter of the triangle is 73 cm, we can write the equation as:
2x + (x/2) + 3 + (x/2) + 3 = 73
Now, we can solve the equation to find the value of x and then calculate the measure of each side.
Combining like terms:
2x + x/2 + x/2 + 3 + 3 = 73
Multiplying each term by 2 to eliminate the fraction:
4x + x + x + 6 + 6 = 146
Combining like terms again:
6x + 12 = 146
Subtracting 12 from both sides:
6x = 134
Dividing both sides by 6:
x = 134/6 = 22.33
Therefore, the measure of each leg of the isosceles triangle is approximately 22.33 cm.
To find the measure of the base, we can use the earlier equation:
base = (x/2) + 3 = (22.33/2) + 3 ≈ 16.17 cm
So, the measure of each side of the triangle is approximately 22.33 cm (legs) and 16.17 cm (base).