the perimeter of an isosceles triangle is 21 meters. the length of one side is 3 meters longer than the length of the other two sides. find the length of each side.

sides : x, x , 21-2x

"the length of one side is 3 meters longer than the length of the other two sides"

This is ambiguous

1st interpretation:

----> 21-2x = x+x+3
-4x = -18
x = 4.5

sides are 4.5, 4.5, and 12
This is not a possible triangle.
To have a triangle the longest side must be less than the sum of the other two sides,

2nd interpretation:

---> 21-2x = x+3
-3x = -18
x = 6
sides are 6, 6, and 9

This one works.

Why did the isosceles triangle go to therapy? Because it couldn't handle all the sideshow drama!

Okay, let's solve this puzzle. Let's assume the length of the two congruent sides is "x". Since the length of one side is 3 meters longer, we can say the other side is "x - 3".

Now, let's calculate the perimeter:

Perimeter = Length of first side + Length of second side + Length of third side

21 = x + x + (x - 3)

Simplifying further, we get:

21 = 3x - 3

Adding 3 to both sides, we have:

24 = 3x

Finally, dividing both sides by 3, we find:

x = 8

Therefore, the length of the two congruent sides is 8 meters, and the length of the remaining side is 5 meters (8 - 3).

Let's assume that the length of the two equal sides of the isosceles triangle is x.

According to the given information, the length of one side is 3 meters longer than the other two sides.

So, the length of the third side is x + 3.

The perimeter of a triangle is calculated by adding the lengths of all three sides.

Therefore, we can write the equation:

x + x + x + 3 = 21

Simplifying this equation, we get:

3x + 3 = 21

Subtracting 3 from both sides:

3x = 18

Dividing both sides by 3:

x = 6

So, the length of the two equal sides is 6 meters, and the length of the third side is 6 + 3 = 9 meters.

To find the length of each side of the isosceles triangle, let's use algebra.

Let's assume that the length of the two equal sides is x, and the length of the third side (which is longer) is x + 3.

The perimeter of a triangle is the sum of the lengths of all its sides. In this case, the perimeter is given as 21 meters.

So we can set up an equation:

x + x + (x + 3) = 21

Combining like terms, we simplify the equation:

3x + 3 = 21

Next, we isolate the variable by subtracting 3 from both sides:

3x = 21 - 3

3x = 18

Finally, we solve for x by dividing both sides by 3:

x = 18 / 3

x = 6

Now that we have the value of x, we can find the length of each side:

The length of the two equal sides is x, so they are both 6 meters.

The length of the third side is x + 3, so it is 6 + 3 = 9 meters.

Therefore, the length of each side of the isosceles triangle is 6 meters, 6 meters, and 9 meters.