Only #'s 24,26,28,&30

Algebra
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Jan 8th, 2015

24 .  sides of right triangles are 6 , 3 , x

using pyhagorean theorem

x^2 = 6^2 + 3^2

     = 36 + 9

    = 45

   = 3 sq.rt 5

26.   first find thirdside of first triangle using pyhagorean theorem

= sq.rt.(5^2 - 3^2)

= 4

unkown side of second triangle =sq.rt.( 4^2 + 7^2)

                                                   = sq. rt. (28 + 49)

                                                   = sq.rt.77

28.     using pyhagorean theorem

(4x - 4)^2 = (2x)^2 + (2x +4)^2

16x^2 - 32x + 16 = 4x^2 + 4x^2 +16x + 16

16x^2 - 8x^2 - 32x - 16x = 0

8x^2 - 48x = 0

8x(x - 6) = 0

 x = 0  or x - 6 = 0 

x = 0 rejected side can't be 0

x = 6

30.   if first part of base = y second part wil be 14 - y

using pyhagorean theorem in both triangles 

x^2 = 13^2 - y^2

x^2 = 15^2 - (14 - y)^2

13^2 - y^2 = 15^2 - (14 - y)^2

169 - y^2 = 225 - 196 + 28y - y^2 

y = 5

 x^2 = 13^2 - y^2 , substitute y = 5

  x^2 = 169 - 25 = 144

x = 12

                                                  


Jan 8th, 2015

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