Two noncongruent triangles have equal area. One triangle has sides 5, 5, and 4. The other has sides 5, 5, and x. Find the value of x.
I managed to get a quadratic equation, but I have no idea how to solve it. Any tips here?
Now use the cosine rule. You are told that one of the two triangles (say the one with angle ) has the third side equal to 4. The cosine rule says that . For the other triangle, with third side x and angle , the formula says . But and are supplementary, and so . Therefore . That's your quadratic equation. Now all you have to do is to solve it.