Question

Help with these two questions, 100 points!!

Answer 1

15. x = 4

16. x = 7

Explanation:

15.

CD/ ED = DG / DF

48 / (5x - 2) = 40 / (2x + 7)

48 (2x + 7) = 40 (5x - 2)

96x + 336 = 200x - 80

200x - 96x = 336 + 80

104x = 416

x = 4

16.

ST / PL = TU / LM

(x + 1) / 72 = (2x - 3) / 99

99 (x + 1) = 72 (2x - 3)

99x + 99 = 144x - 216

144x - 99x = 99 + 216

45x = 315

x = 7

Answer 2

15. x = 4

16. x = 7

Explanation:

Similar Triangles

In similar triangles, corresponding sides are always in the same ratio.

Question 15

If ΔCDG ~ ΔEDF then:

• CD : ED = DG : DF = CG : EF

From inspection of the given diagram:

• CD = 48
• ED = 5x - 2
• DG = 40
• DF = 2x + 7

Therefore:

`\implies \sf CD : ED = DG : DF`

`\implies 48 : (5x-2) = 40 : (2x+7)`

`\implies (48)/((5x-2)) = (40)/((2x+7))`

`\implies 48(2x+7)=40(5x-2)`

`\implies 96x+336=200x-80`

`\implies 416=104x`

`\implies x=(416)/(104)`

`\implies x=4`

Question 16

If ΔSTU ~ ΔPLM then:

• ST : PL = TU : LM = SU : PM

From inspection of the given diagram:

• ST = x + 1
• PL = 72
• TU = 2x - 3
• LM = 99
• PM = 70

Therefore:

`\implies \sf ST : PL = TU : LM`

`\implies (x+1) : 72 = (2x-3) : 99`

`\implies ((x+1))/(72)= ((2x-3))/(99)`

`\implies 99(x+1)=72(2x-3)`

`\implies 99x+99=144x-216`

`\implies 315=45x`

`\implies x=(315)/(45)`

`\implies x=7`