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In the trapezoid shown, the ratio of the area of triangle ABC to the area of triangle ADC is 7 : 3. If AB + CD = 210 cm, how long is segment \(\overline{AB}\)?

 Apr 6, 2019
edited by Logic  Apr 6, 2019
 #1
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AB + CD = 210   ⇒  CD = 210 - AB

 

Both triangles ACD and ABC are under the same height  ...so....

 

Area of triangle ACD                 3

_________________  =      ______

Area of triangle  ABC                7

 

 

(1/2) h (CD)              3

__________  =       ____

(1/2) h ( AB)              7

 

 

CD                  3

___    =          __

AB                  7

 

       

210 - AB                3

_______   =        ____     cross-multiply

   AB                       7

 

 

7( 210 - AB )  =   3(AB)       simplify 

 

1470  - 7AB  =  3AB       add  7AB to both sides

 

1470  =  10AB                divide both sides by  10

 

147  = AB 

 

 

cool cool cool

 Apr 6, 2019
edited by CPhill  Apr 6, 2019

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