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2 years ago

5

GeometryNeed help finding A and B

1 answer:

MariettaO [177]2 years ago

4 0

Answer:

a = 8

b = 4√5

Step-by-step explanation:

Corresponding sides of similar triangles are proportional.

short side/long side = a/16 = 4/a

a² = 64 . . . . . . multiply by 16a

a = 8 . . . . . . take the square root

__

hypotenuse/short side = b/4 = 20/b

b² = 80 . . . . . . . multiply by 4b

b = 4√5 . . . . . take the square root

_____

<em>Additional comment</em>

These relations for the right triangle can be summarized by the rule "the length of a segment that touches the hypotenuse is the geometric mean of the two hypotenuse segments it touches." In the case of b, that means ...

b = √((4)(4+16)) = 4√5

The same sort of relation applies to the unmarked vertical segment on the left:

c = √((16)(16+4)) = 8√5

And, we saw ...

a = √((4)(16)) = 8

Of course, if this rule is to make sense, you need to know that the geometric mean of two numbers is the square root of their product. (In general, the geometric mean of n numbers is the n-th root of their product.)

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Answer:

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