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csciahetano
09.01.2020 •
Mathematics
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?
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Ответ:
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
Ответ:
Step-by-step explanation:
x-number of hours after which the cost would be the same