△ABC△ABC is isosceles. The two congruent sides are 5x + 23 and 2x + 32. The other side is 8.
Solve for the value of x and then find the perimeter.
since the congruent sides have equal lengths,
5x+23 = 2x+32
Find x and let 'er rip.
To solve for the value of x in this isosceles triangle, we can set the two congruent sides equal to each other and solve for x.
5x + 23 = 2x + 32
To isolate x, we can begin by subtracting 2x from both sides:
5x - 2x + 23 = 2x - 2x + 32
This simplifies to:
3x + 23 = 32
Next, we can subtract 23 from both sides:
3x + 23 - 23 = 32 - 23
3x = 9
Now, we can solve for x by dividing both sides by 3:
3x / 3 = 9 / 3
This gives us:
x = 3
So, the value of x is 3.
Now, to find the perimeter of the triangle, we need to add up the lengths of all three sides.
The two congruent sides are 5x + 23 and 2x + 32, so substituting x = 3, we can find their lengths:
Length of congruent side = 5(3) + 23 = 15 + 23 = 38
Length of other congruent side = 2(3) + 32 = 6 + 32 = 38
The length of the third side is given as 8.
Thus, the perimeter of the triangle is:
Perimeter = Length of congruent side + Length of other congruent side + Length of third side
= 38 + 38 + 8
= 84
Therefore, the perimeter of the triangle is 84 units.