Find the longest side of triangle ABC, if measurement A=70, measurement B=2x-10, and measurement C=3x+20.

I will assume that by "measurement A=70" you are referring to angle A

then 70 + 2x-10 + 3x+20 = 180
5x = 100
x = 20

then angle B = 30 and
angle C = 80

knowing that in any triangle, the largest side is opposite the largest angle, the largest side must be opposite angle C, which would be AB

reiny is correct

y'all homies wrong

To find the longest side of triangle ABC, we need to compare the lengths of all three sides.

Given that the measurements of the sides are A=70, B=2x-10, and C=3x+20, we can set up the following inequalities to compare their lengths:

A < B + C
B < A + C
C < A + B

Let's solve these inequalities step by step:

1. A < B + C:
Substituting the given values, we get:
70 < (2x-10) + (3x+20)
70 < 5x + 10x + 10
70 < 15x + 10
70 - 10 < 15x
60 < 15x
4 < x

2. B < A + C:
Substituting the given values, we get:
(2x-10) < 70 + (3x+20)
2x - 10 < 90 + 3x + 20
2x - 3x < 90 + 20 + 10
-x < 120
x > -120 (division by -1 results in a change in the inequality sign)

3. C < A + B:
Substituting the given values, we get:
(3x+20) < 70 + (2x-10)
3x + 20 < 70 + 2x - 10
3x - 2x < 70 - 20 - 10
x < 40

Now, we need to find the maximum value of x that satisfies all the inequalities.
From inequality 2, we have x > -120, and from inequality 3, we have x < 40.
Therefore, the possible range for x is -119 < x < 40.

We can now calculate the values of B and C using the obtained range of x:

For the minimum value of x (x = -119):
B = 2x - 10 = 2(-119) - 10 = -248
C = 3x + 20 = 3(-119) + 20 = -357

For the maximum value of x (x = 39):
B = 2x - 10 = 2(39) - 10 = 68
C = 3x + 20 = 3(39) + 20 = 137

Finally, we can compare the lengths of A, B, and C:
A = 70
B = -248 (for minimum x) or 68 (for maximum x)
C = -357 (for minimum x) or 137 (for maximum x)

From these values, we can see that the longest side of triangle ABC is side C, which has a length of 137 (for the maximum value of x).

5x-10=80 x=16

B=2(16) - 10 = 22

C= 3(16)+20 = 68

I'm not sure if that's right or not.

Find the pattern

Give the formula

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