Question

HW #35: similar polygons

Answer 1

Answer:

Q 9:

Because the two polygons are similar so AB ≈ PQ = SR

Scale factor is 25/20 = 1.25

Perimeter of ABCD = 14+20+14+20 = 68

We can find the length of SP by multiplying the scale factor with the AD so

SP = 14 * 1.24= 17.5

Perimeter of PQRS = 17.5+25+17.5+25 = 85

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Q 10:

Because the two polygons are similar so AD ≈. EH

Scale factor is 7/14 = 0.5

Perimeter of ABCD = 12+14+13+26 = 65

Because the two polygons are similar so DC ≈ HG

and our scale factor is 0.5 so HG = 13/2 = 6.5

Perimeter of EFHG = 6 + 7 + 6.5 + 13 =  32.5

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Q 11:

The Geometric Mean is a special type of average where we multiply the numbers together and then take a square root (for two numbers). And the formula for finding the Geometric mean of two numbers a and b is

$\sqrt{a*b}$

So geometric mean of the 8 and 10 can be found as

$\sqrt{8*2} = \sqrt{16} = 4$

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Q 12:

Similarly we can using the above formula of finding the geometric mean of 5 and 45 as

$\sqrt{5*45} = \sqrt{225} = 15$

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Q 13:

and we can find the geometric mean of 6 and 30 by using the same formula

$\sqrt{6*30} = \sqrt{180} = 13.41$