How to find the height of a right triangle - PSAT Math
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Question
Note: Figure NOT drawn to scale.
Refer to the above diagram. Give the ratio of the perimeter of 
to that of 
.
Note: Figure NOT drawn to scale.
Refer to the above diagram. Give the ratio of the perimeter of
Answer
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 of to that of is
or 
: 1,
so this is also the ratio of the perimeter of to that of .
The altitude of a right triangle from the vertex of its right triangle to its hypotenuse divides it into two similar triangles.
The ratio of the smaller sides of these similar triangles is
The ratio of the smaller side of
so this is also the ratio of the perimeter of
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