Question

Please help with questions 17-19

Answer 1

17) x= 13.6 cm

18) Perimeter of Δ DEF =56 cm

19) Area of Δ DEF 168 cm²

Explanation:

17) As Δ ABC↔ΔDEF

m AB↔ m DE

mBC↔ mEF

25: 20

17:x

x= 20*17/25=340/25=13.6 cm

18) let the third side of the triangle be y

25:20

28:y

y=20*28/25= 560/25= 22.4 cm

Perimeter of a triangle DEF = x+y+ 20= 13.6+22.4+20= 56 cm

19) Perimeter of Δ ABC= 28+17+25= 70 cm

Let z be the area of ΔDEF then

210:z

70:56

z=210*56/70= 168 cm²

Answer 2

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.