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Triangle ABC is translated to create triangle DFG, as shown below.
2y + 12 cm
212y - 3) cm
312x + 10) cm
12x + 12 cm
G
In these triangles, side AB is congruent to side DF, and side BC is congruent to side FG. Determine the values of x
andy
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Triangle ABC is translated to create triangle DFG as shown below 2y 12 cm 212y 3 cm 312x 10 cm 12x 12 cm G In these triangles side AB is congruent to side DF an class=

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MrRoyal

Answer:

[tex]x=3[/tex]

[tex]y = 9[/tex]

Step-by-step explanation:

Given

The translated triangles

Required

Find x and y

We have:

[tex]AB = DF[/tex]

[tex]BC = FG[/tex]

[tex]AB = DF[/tex] means:

[tex]3(2x + 10) = 12x + 12[/tex]

Open bracket

[tex]6x + 30 = 12x + 12[/tex]

Collect like terms

[tex]12x - 6x = 30 -12[/tex]

[tex]6x = 18[/tex]

Divide by 6

[tex]x=3[/tex]

[tex]BC = FG[/tex] means

[tex]2y + 12 = 2(2y - 3)[/tex]

Open bracket

[tex]2y + 12 = 4y - 6[/tex]

Collect like terms

[tex]4y - 2y = 12+6[/tex]

[tex]2y = 18[/tex]

Divide by 2

[tex]y = 9[/tex]

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