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3 years ago

9

A solid has faces that consist of 5 congruent squares and 4 congruent equilateral triangles. The solid has 9 vertices. How many

edges does the solid have? (no image)
A.
16 edges
B.
18 edges
C.
20 edges
D.
22 edges

1 answer:

zimovet [89]3 years ago

8 0

The answer is <span>A. 16 edges

For most of the solid shapes, we can use Euler's polyhedron formula:
f + v - e = 2
f - the number of faces
v - the number of vertices
e - the number of edges

We know:
f = 5 + 4 = 9
v = 9
e = ?

So:
</span>f + v - e = 2
9 + 9 - e = 2
18 - e = 2
18 = e + 2
e = 18 - 2
e = 16

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3 years ago

Read 2 more answers

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Explanation contains the proof.

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$b-5=8m \text{ gives us } b=8m+5$ .

So back to $ab$ ....

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$=(8k+5)(8m+5)$

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Factoring out 8 gives us:

$=8(8km+5k+5m)+25$

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We have shown that there is integer $n \text{ such that } ab=8n-1$ .

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