In a right-angled triangle ABC, the angle is C = 90 degrees; BC = 12 cm Point E lies on the leg AC
| July 5, 2021 | education
In a right-angled triangle ABC, the angle is C = 90 degrees; BC = 12 cm Point E lies on the leg AC, point F belongs to the hypotenuse AB, and EF is perpendicular to AB. AE = 10 cm, EF = 6cm. Find the hypotenuse AB.
Since, by condition, EF is perpendicular to AB, then triangle AEF is rectangular.
In right-angled triangles ABC and AEF, the angle A is common, then these triangles are similar in acute angle.
From the similarity of triangles: BC / AB = EF / AE.
AB = BC * AE / EF = 12 * 10/6 = 20 cm.
Answer: The length of the hypotenuse AB is 20 cm.
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