Question

In the following figure, triangle ABC and triangle DEF are similar. What is the value of x ? Triangle ABC and triangle DEF are shown. Side AB measures 10 millimeters. Side BC measures 4 millimeters. Side CA measures 8.5 millimeters. Side DE is not labeled. Side EF measures 12 millimeters. Side FD measures x. (1 point) x = 16.5 mm x = 24 mm x = 25.5 mm x = 30 mm

Answer 1

The answer is x = 30 mm.

Similar shapes have proportional measurements. Hence:
side AB/side BC = side DE/side EF

1.) Substitute with given:
     AB/BC = DE/EF
         10/4 = DE/12

2.) Cross multiply 10/4 = DE/12
         4DE = 120

3.) Divide both sides of the equation by 4 to solve for DE:
      4DE/4 = 120/4
           DE = 30 mm.

4.) Substitute and cross multiply to check if the values are equal:
     AB/BC = DE/EF
         10/4 = 30/12
        4(30) =10(12)
          120 = 120