Question

Find all values of $x$ that make the triangles congruent. Two triangles ABC and DBC with a common base BC. In triangle ABC, AC measures 4x minus 7 and AB measures 2x plus 3. In triangle DBC, DB measures 2x plus 1 and DC measures 3x minus 1.

Answer 1

To find the values of x, set the lengths of the corresponding sides of the two triangles equal to each other and solve for x =4.

We are given two triangles, ABC and DBC, with a common base BC. In triangle ABC, side AC is represented by 4x-7 and side AB is represented by 2x+3. In triangle DBC, side DB is represented by 2x+1 and side DC is represented by 3x-1.

To find the values of x, we can set the lengths of the corresponding sides equal to each other and solve for x. So, we have:

4x-7 = 2x+1 (lengths of AC and DB)

2x+3 = 3x-1 (lengths of AB and DC)

Solving these equations, we find x = 4 and x = 4, respectively. Therefore, the value of x is 4.

The complete question is- Consider two triangles, ABC and DBC, sharing a common base BC. In triangle ABC, the length of side AC is represented by 4x−7, and the length of side AB is represented by 2x+3. In triangle DBC, the length of side DB is represented by 2x+1, and the length of side DC is represented by 3x−1.

Determine all values of x for which the two triangles, ABC and DBC, are congruent.