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AshBorg
21.01.2020 •
Mathematics
The altitude to the hypotenuse of a right triangle divides the hypotenuse into segments with lengths in the ratio 1 : 2. the length of the altitude is 8. how long is the hypotenuse?
a. 16
b. 24
c. ![4\sqrt{2}](/tex.php?f=4\sqrt{2})
d. ![6\sqrt{6}](/tex.php?f=6\sqrt{6})
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Ответ:
a) The length of the hypotenuse = 16 units.
Step-by-step explanation:
Here, let us assume the given right angle triangle is Δ ABC.
Here. AC is the hypotenuse, which is divided in the ratio 1: 2 by the altitude BM.
⇒ AM : MC = 1: 2
Let us assume the common ratio = x
⇒ AM = x and MC = 2 x
Also. AM = 8 units
Solving this by common ratio of sides, we get:
Hence, AM = 4√2 , MC = 2 (4√2)
⇒ AC = 12√2 units ≈ 16 units
Hence, the length of the hypotenuse = 16 units.
Ответ:
the answer x=15. Hope this helps!