The following triangle has sides of length , , and as shown. Choose the compound inequality which must be true based on the sides of the triangle.

Question

The following triangle  has sides of length  ,  , and  as shown.  Choose the compound inequality which must be true based on the sides of the triangle.

Quizplus · Accepted Answer

In any triangle, the sum of the lengths of any two sides must be greater than the length of the third side. Using this rule, we can write the following inequalities:
11ec1544_374a_a56d_8a2d_a9cbf77d1f8a_TBX8671_11 + 11ec1544_374a_a56e_8a2d_51567f46fab2_TBX8671_11 > 11ec1544_374a_a56f_8a2d_c1629bdf92cf_TBX8671_11
11ec1544_374a_a570_8a2d_4b1ca006b9c9_TBX8671_11 + 11ec1544_374a_a571_8a2d_d21d48fbd824_TBX8671_11 > 11ec1544_374a_a572_8a2d_23942c7d22ef_TBX8671_11
11ec1544_374a_a573_8a2d_601f5293d3c5_TBX8671_11 + 11ec1544_374a_a574_8a2d_f0eed09b8717_TBX8671_11 > 11ec1544_374a_a575_8a2d_95225b8dccb3_TBX8671_11
Simplifying these expressions, we get:
11ec1544_374a_c86d_8a2d_d1cf13e7801b_TBX8671_11 > 0
This compound inequality must be true, since the sum of any two sides of a triangle must be greater than the third side.

The Following Triangle Has Sides of Length