Answer:
The side lengths of the first triangle are:
[tex]|AB|=30[/tex]
[tex]|BC|=29[/tex]
[tex]|AC|=22[/tex]
The side lengths of the second triangle are:
[tex]|PQ|=22[/tex]
[tex]|QR|=22[/tex]
[tex]|PR|=37[/tex]
Step-by-step explanation:
The perimeter of the first triangle is:
[tex]P_{1}=2x+8+2x+2x+7[/tex]
and the second perimeter is:
[tex]P_{2}=2x+2x+3x+4[/tex]
Now, we know the perimeters are equal.
[tex]P_{1}=P_{2}[/tex]
[tex]2x+8+2x+2x+7=2x+2x+3x+4[/tex]
[tex]x=11[/tex]
The side lengths of the first triangle are:
[tex]|AB|=2(11)+8=30[/tex]
[tex]|BC|=2(11)+7=29[/tex]
[tex]|AC|=2(11)=22[/tex]
The side lengths of the second triangle are:
[tex]|PQ|=2(11)=22[/tex]
[tex]|QR|=2(11)=22[/tex]
[tex]|PR|=3(11)+4=37[/tex]
I hope it helps you!
