Using the altitude theorem. i have a triangle, the altitude is 20. a is 25 but there's no b. just the sum of a and b which is x. how do i solve this problem?

Step-by-step explanation:

We're given a right triangle with an altitude h = 20 that divides the hypotenuse into two segments a and b, and given a = 25 and a + b = x.

The altitude theorem states that h = sqrt(a*b), or equivalently that h^2 = a*b. We already know what a and h are; now let's solve for b.

a + b = x

a + b - a = x - a

b = x - a

So then

h^2 = a*b

h^2 = a*(x - a)

h^2 = ax - a^2

20^2 = 25x - 25^2

400 = 25x - 625

400 + 625 = 25x - 625 + 625

1025 = 25x

1025/25 = 25x/25

x = 41

Now we plug this back into our equation for b.

b = x - a

b = 41.- 25

b = 16

We can verify that this is the correct answer using the altitude theorem.

h^2 = a*b

20^2 = 25*16

400 = 400

a 4/6 = 9/12   not proportional

step-by-step explanation:

to find which are not proportional, we can use cross products

if it is true, they are proportional.   if it is not true, they are not proportional.

a 4/6 = 9/12

4* 12 = 6*9

48 = 54

not this is not proportional  

b 2/3 = 12/18  

2* 18 = 3 * 12

36 = 36

this is proportional

c 5/4 = 10/8  

5*8 = 4*10

40 = 40

this is proportional

d 7/5 = 35/25

7*25 = 5 * 35

175 = 175

is proportional