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Find the missing length indicated

 

 Jul 11, 2020
 #1
avatar+1130 
+2

we can use the pythagorenas theorem to find the altitude is 60 and we have te equation 60^2+x^2=y^2 and (x+25)^2-65^2=y^2 where y is the base 

 Jul 11, 2020
 #2
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+1

In the small right triangle on the RHS with sides of 65 and 25, wil find the altitude by Pythagoras's Theorem:
65^2 =25^2 + A^2
A  =sqrt(3600) =60
The measure of the altitude drawn from the vertex of the right angle of a right triangle to its hypotenuse is the geometric mean of the measures of the two segments of the hypotenuse.
Sqrt(25x) =60
5sqrt(x) =60      Divide both sides by 5
sqrt(x) =12         Square both sides
x = 144

 Jul 11, 2020
 #3
avatar+31087 
+1

As follows:

Solve for x.

 Jul 11, 2020
edited by Alan  Jul 11, 2020
 #4
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0

I think Alan made a typo. You can't solve for x in the last equation! 

 

Cos(25/65) = 65 /(x + 25) - Now you can solve for x

169 =x + 25

x =169 - 25 = 144

 Jul 11, 2020
 #6
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0

Hello, Guest!

Alan's equation is solvable; it just takes more time, but the result is the same.

 

65 / x+25 = 25 / 65

 

Step 1: Cross-multiply.

 

65 * 65 = 25 * x+25

 

4225 = 25x + 625

 

Step 2: Flip the equation.

 

25x + 625 = 4225

 

Step 3: Subtract 625 from both sides.

 

25x + 625−625 = 4225−625

 

25x = 3600

 

Step 4: Divide both sides by 25.

 

25x / 25 = 3600 / 25

 

x = 144

Guest Jul 11, 2020
 #5
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0

h = sqrt (65- 252) = 60

 

25 / 60 = 60 / x

 

x = 144   

 Jul 11, 2020

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