Answers:
17 -- x = 13.6
18 -- perimeter = 56 cm
19 -- 134.4 cm^2
Showing mah work!
17) This question is asking for a proportion in order to solve for x. The problem says that the two triangles are similar so we can use this set up something that says line AB over BC = line DE over EF and then solve for x when we cross multiply:
17/25 = x/20
Cross-multiply:
25x = 17(20)
Simplify:
25x = 340
Divide both sides by 25 to isolate the variable and satisfy the division property of equality
25x/25 = 340/25
x = 340/25
x = 13.6
18) We can do the same thing to find the length of line DF and then just add up the sides. Let y = line DF. We are going to do line AB over AC = line DE over DF
17/28 = 13.6/y
Cross-multiply:
17y = 13.6(28)
y = (13.6*28)/17
y = 22.4 cm
Now to find perimeter, we just add up the sides. DE + EF + DF.
13.6 + 20 + 22.4 = 33.6 + 22.4 = 56 cm
Note that the units are just centimeters, not centimeters squared. This is foreshadowing for the next question btw
19) Again, the triangles are similar so we can set up a proportion using their bases and cross-mutiply again to find the area of the second triangle. Just gotta do a little modification. Let z = the area of triangle DEF
DF^2 / AC^2 = z / 210
22.4^2 / 28^2 = z / 210
501.76(210) = 784z
(501.76*210)/784 = z, please use a calculator for that.
z = 134.4 cm^2 or 134.4 square centimeters.
You must use square centimeters because we are talking area and not perimeter; multiplication not addition.
