A straight line is drawn through point B of the PK side of the KTP triangle, parallel to the side of the TK
| August 1, 2021 | education
A straight line is drawn through point B of the PK side of the KTP triangle, parallel to the side of the TK side and crossing the PT side at point A. Calculate the length of the segment AB if KT = 52 cm, AT = 12 cm, AP = 36 cm.
Consider triangles TKP and ABP, these triangles are similar in the first sign of similarity of triangles.
∠KPT is the total angle of triangles, ∠KTP = ∠BAP as one-sided angles at the intersection of parallel lines TK and AB.
By definition of similar triangles KT / AB = TB / AP.
CT / AB = (AT + AP) / AP.
52 / AB = (12 + 36) / 36.
AB = 52 * 36/48 = 39 cm.
Answer: Side AB = 39 cm.
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