what is this called: a triangle that has a line in the middle, it is parallel to the bottom but not exactly half, a 4 is on the top part of the triangle (right side) and an X is on the bottom right part of the triangle, the small line has a 3 and the big line has an 8. What is X and what is this type of problem called?

Question

what is this called: a triangle that has a line in the middle, it is parallel to the bottom but not exactly half,  a 4 is on the top part of the triangle (right side) and an X is on the bottom right part of the triangle, the small line has a 3 and the big line has an 8. What is X and what is this type of problem called?

anonymous · Answer

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mani_jha · Answer

The concept is known as similarity of triangles. Do you know it?

anonymous · Answer

that is what its called! wow i am seriously blinded. thank you! how would i solve for x, however?

mani_jha · Answer

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First, try to prove that triangles APQ and ABC are similar. For a similar triangle, the ratios of the corresponding sides are equal. Thus,:
$$AP/AB=AQ/AC=PQ/BC$$
Use the last two terms. Now, can you do it?