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Example Question #81 :Triangles
Note: Figure NOT drawn to scale.
Refer to the above diagram. Give the ratio of the perimeter ofto that of.
Possible Answers:
Correct answer:
Explanation:
The altitude of a right triangle from the vertex of its right triangle to its hypotenuse divides it into two similar triangles.
, as the length of the altitude corresponding to the hypotenuse, is the geometric mean of the lengths of the parts of the hypotenuse it forms; that is, it is the square root of the product of the two:
.
The ratio of the smaller sides of these similar triangles is
The ratio of the smaller side ofto that ofis
or: 1,
所以这也是比率of the perimeter ofto that of.
Pierre
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