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square pyramid has a base side length of 20.4 cm and a height of 18.2 cm. which square pyramid is similar?
a)base side length = 18.2 cm, height = 20.4 cm
b)base side length = 22.9 cm, height = 20.7 cm
c)base side length = 30.6 cm, height = 27.3 cm
d)base side length = 40.8 cm, height = 45.5 cm

The correct option is

(C) base side length = 30.6 cm, height = 27.3 cm

Step-by-step explanation:  Given that a square pyramid has a base length of 20.4 cm and a height of 18.2 cm.

That is, b = 20.4 cm  and h = 18.2 cm.

We are to select the correct options that gives the base length and height of a similar pyramid.

We know that, for two square pyramids to be similar, the corresponding base lengths and the heights must be proportional.

Option (A)

base side length, b' = 18.2 cm  and  height, h' = 20.4 cm.

So, we have

Therefore,

and thus the square pyramid (A) is not similar to the given square pyramid.

Option (B)

base side length, b' = 22.9 cm  and  height, h' = 20.7 cm.

So, we have

Therefore,

and thus the square pyramid (B) is not similar to the given square pyramid.

Option (C)

base side length, b' = 30.6 cm  and  height, h' = 27.3 cm.

So, we have

Therefore,

and thus the square pyramid (C) is SIMILAR to the given square pyramid.

Option (D)

base side length, b' = 40.8 cm  and  height, h' = 45.5 cm.

So, we have

Therefore,

and thus the square pyramid (D) is not similar to the given square pyramid.

Hence, the correct option is

(C). base side length = 30.6 cm, height = 27.3 cm.

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step-by-step explanation:

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