The height drawn to the hypotenuse AC of the right-angled triangle ABC
| June 19, 2021 | education
The height drawn to the hypotenuse AC of the right-angled triangle ABC divides it into segments equal to 25cm and 9cm. What is the larger leg of triangle ABC?
According to the property of the height of a right-angled triangle, drawn from the vertex of the right angle, the length of the height is equal to the square root of the product of the segments into which the height divides the base.
BH = AD * CD = 25 * 9 = 225 = 15 cm.
From a right-angled triangle ABD, by the Pythagorean theorem, we determine the length AB.
AB ^ 2 = AD ^ 2 + BD ^ 2 = 252 + 152 = 625 + 225 = 850.
AB = √850 = 5 * √34 cm
Answer: The length of the larger leg is 5 * √34 cm.
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