the shortest side on a isosceles triangle is 2x-3 inches long. the two longer sides are 6 inches longer than the shortest side.the perimeter of the triangle is 33 inches. what is the length of each of the longer sides of the triangle
s+ s+6 + s+6 = 33
3 s + 12 = 33
3 s = 21
s = 7
s+6 = 13 indeed
^^^according to the qiuz I am definantly not cheating on the options are 4, 13, -4, -13. So I assume it is 13
wait is it 13
thank you
now to prove it without asking me
if s = 7
then the sides are
7 13 13
and sum is 26+7 = 33
whew !
You are welcome :)
To find the length of each of the longer sides of the triangle, we can start by identifying the variables and setting up equations based on the given information.
Let's say the shortest side of the triangle is represented by the variable "a" (2x-3 inches long). Both of the longer sides are 6 inches longer than the shortest side, so we can represent them as "a+6".
The perimeter of a triangle is the sum of the lengths of all three sides. In this case, the perimeter is given as 33 inches.
So, we can set up the equation:
a + (a+6) + (a+6) = 33
Now, we can solve for "a".
Substituting "2x-3" for "a" in the equation:
(2x-3) + (2x-3+6) + (2x-3+6) = 33
Simplifying the equation:
2x - 3 + 2x + 3 + 2x + 3 = 33
6x + 3 = 33
Subtracting 3 from both sides:
6x = 30
Dividing both sides by 6:
x = 5
Now that we have the value of "x", we can substitute it back into the equation to find the length of each longer side.
Shortest side (a) = 2x - 3
Substituting x=5:
a = 2(5) - 3 = 10 - 3 = 7 inches
Length of each longer side = a + 6
Substituting a=7:
Length of each longer side = 7 + 6 = 13 inches
Therefore, the length of each of the longer sides of the triangle is 13 inches.