The lengths of the sides of a triangle are 3x, 5x – 12, and x + 20. Find the value of x so that the triangle is isosceles.
Can somebody show me a step-by-step process of how to get the answer(s) please? I need it:) I also saw that x could = 8, 10, and 6. Is this true? How so? Thanks!
Any two side are equal in isoscles triangle
5x-12=x+20
4x=32
x=8
5x-12=28
x+20=28
5x=40
28,28,40
for those still there looking for it
I’m confused, Is their one singular answer or is it the multiple answers? I got x=8, x=10, & x=6 but i don't know which one to use. Plus we don't have enough information to assume which sides are the congruent ones, so do I put all three of these as the answer?
all the answers are making me even more confused
Depends which are the two equal sides
case1: 5x - 12 = 3x
2x = 12
x = 6
then the sides are 18, 18 and 26
case2: 3x = x+20
2x = 20
x = 10
then the sides are 30, 30 and 38
case3: 5x-12 = x+20
4x = 32
x = 8
then the sides are 24, 28 and 28
I don't understand how this problem can have three different answers. These were the answers i go and i don't see anything else that could relate any of the angles together. So would all of them be correct or just one??
The lengths of the sides of a triangle are
3
x
,
5
x
−
12
,
and
x
+
20
.
Find the value of x so that the triangle is isosceles.
i have her too lol
im stuck
To find the value of x that makes the triangle isosceles, we need to find the value of x for which two sides of the triangle are equal in length.
Step 1: Set up the equation
For an isosceles triangle, two sides must be equal. Let's set up the equation to represent this:
3x = 5x - 12
Step 2: Solve the equation
Now we can solve the equation to find the value of x.
Subtract 3x from both sides of the equation to isolate the variable:
3x - 3x = 5x - 12 - 3x
0 = 2x - 12
Add 12 to both sides of the equation:
12 = 2x - 12 + 12
12 = 2x
Divide both sides of the equation by 2:
12/2 = 2x/2
6 = x
So, x = 6
Step 3: Check the solution
To verify if x = 6 makes the triangle isosceles, substitute x = 6 in the given lengths of the triangle:
Side 1 = 3x = 3(6) = 18
Side 2 = 5x - 12 = 5(6) - 12 = 18 - 12 = 6
Side 3 = x + 20 = 6 + 20 = 26
As we can see, Side 1 (18) is equal to Side 2 (6), so the triangle is isosceles when x = 6.
Regarding the additional values you mentioned (x = 8, 10, and 6), let's check if they indeed make the triangle isosceles:
For x = 8:
Side 1 = 3x = 3(8) = 24
Side 2 = 5x - 12 = 5(8) - 12 = 40 - 12 = 28
Side 3 = x + 20 = 8 + 20 = 28
In this case, Side 1 (24) is not equal to Side 2 (28), so x = 8 does not make the triangle isosceles.
For x = 10:
Side 1 = 3x = 3(10) = 30
Side 2 = 5x - 12 = 5(10) - 12 = 50 - 12 = 38
Side 3 = x + 20 = 10 + 20 = 30
Again, Side 1 (30) is not equal to Side 2 (38), so x = 10 does not make the triangle isosceles.
For x = 6 (as previously calculated):
Side 1 = 3x = 3(6) = 18
Side 2 = 5x - 12 = 5(6) - 12 = 30 - 12 = 18
Side 3 = x + 20 = 6 + 20 = 26
Here, Side 1 (18) is indeed equal to Side 2 (18), so x = 6 makes the triangle isosceles.
Thus, the correct value of x that makes the triangle isosceles is x = 6.