Question

This is my 5star hw please help me​

Answer 1

1) z=?

using similar triangles:

x / z = (8+x) / 20

20x / (8+x) = z since x=8

z = 20(8) / (8+8) = 160 / 16 = 10

or

Midsegment theorem:

z = (1/2)(20) = 10

2) x = (1/2)(13) = 6.5

or

ratio of similar triangles:

4/ x = 8/13

x = 4(13)/8 = 6.5

3) x = 2(10) = 20

or

similar triangles:

a/10 = 2a/x

ax = 20a

x = 20

4) a/5 = 2a/(x+1)

a(x+1) = 10a

x+1 = 10

x = 10 -1 = 9

5)

similar triangles:

a/31 = 2a/2x

a(2x) = 62a

2x = 62

x = 31

midsegment theorem:

2x = 2(31)

2x = 62

x = 31