The shortest side of an isosceles triangle is labeled, in inches, in the triangle below. The two longer sides are 6 inches longer than the shortest side. The perimeter of the triangle is 33 inches.
Picture shows an isosceles triangle with 2x-3 under it
What is the length of each of the longer sides of the triangle?
Show your work.
im so confused pls help
you know that the perimeter is the sum of all the sides, right? So now you have
each long side is 6 more than 2x-3 or 2x+3
2x-3 + 2x+3 + 2x+3 = 33
6x+3 = 33
6x=30
x = 5
So, each long side is 2(5)+3 = 13
Check: 7+13+13 = 33
To find the length of each of the longer sides of the isosceles triangle, we can use the information given about the shortest side and the perimeter of the triangle.
Let's denote the length of the shortest side as x inches.
According to the given information, the two longer sides are 6 inches longer than the shortest side. So, the length of each longer side would be x + 6.
The perimeter of a triangle is the sum of the lengths of all its sides. In this case, the perimeter is given as 33 inches. Since the triangle is isosceles, we can write the perimeter equation as:
x + (x + 6) + (x + 6) = 33.
Simplifying the equation:
3x + 12 = 33,
3x = 33 - 12,
3x = 21.
Dividing both sides by 3:
x = 7.
Now we can find the length of each of the longer sides:
x + 6 = 7 + 6 = 13.
Therefore, each of the longer sides of the triangle has a length of 13 inches.
In summary:
Shortest side length: x = 7 inches.
Length of each longer side: x + 6 = 7 + 6 = 13 inches.