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A right triangle with a perimeter of 60 units has an altitude (to the hypotenuse) of length 10 units. Find the sum of the lengths of the two (non-hypotenuse) legs of this triangle.

 Jan 18, 2022
 #1
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https://web2.0calc.com/questions/geometry_84069#r1

 Jan 18, 2022
 #5
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Using this equation, we can calculate the length of a longer leg:  b ≈ 23.204

Let's see if this equation works:

Angle A = 25.528 degrees

c = sqrt(b2 - 102) + tan(A) * 10

c ≈ 25.714

a = sqrt(c2 - b2)

a ≈ 11.082

a + b + c = 11.082 + 23.204 + 25.714 = 60

Guest Jan 18, 2022
 #2
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according to the pythagorean theorem, a^2 + b^2(the two legs) = c^2

 

we also know that a + b + c = 60

a + b = 50

a^2 + b^2 = 100

(a+b)^2 = 50^2: a^2+b^2+2ab = 2500

 

 

a + b = 50

a*b = 2400

 

you can solve from there to get the two legs. 

 Jan 18, 2022
 #4
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What makes you think that a+b = 50 ? Would you explain, please?

Guest Jan 18, 2022
 #3
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a + b + c = 60

 Jan 18, 2022

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