write a compound inequality that gives the possible lengths, x, of the side of the triangle.
the tringle sides are: 10 in, 12 in, and x.
the answer is 2<x<22
can someone tell me how to get the answer?
+23254 THe legnths of any two sides of a triangle, when added together, must be longer than the third side.
So: 10 + x > 12 ---> x > 2 ---> 2 < x
And: 10 + 12 > x ---> 22 > x ---> x < 22
And: 12 + x > 10 ---> x > -2 (Since, by the first inequality, x > 2; for x to be both > -2 and > 2, it must be > 2, so we'll throw away this answer.)
Since 2 < x and x < 22, we get: 2 < x < 22
+23254 THe legnths of any two sides of a triangle, when added together, must be longer than the third side.
So: 10 + x > 12 ---> x > 2 ---> 2 < x
And: 10 + 12 > x ---> 22 > x ---> x < 22
And: 12 + x > 10 ---> x > -2 (Since, by the first inequality, x > 2; for x to be both > -2 and > 2, it must be > 2, so we'll throw away this answer.)
Since 2 < x and x < 22, we get: 2 < x < 22
