The of a is the sum of its three sides.
△ABC has the sides
2x, 2x+4, and
2x+3. Adding these, we can create an that describes the perimeter of the triangle.
P△ABC=2x+(2x+4)+(2x+3)=6x+7
The triangle
△PQR has the sides
3x+1, 2x, and
2x. We can create an expression for the perimeter of this triangle as well.
P△PQR=(3x+1)+2x+2x=7x+1
Since the perimeters are equal, we can equate the expressions, and solve for
x.
Knowing that
x=6, we can find the side lengths of both triangles by substituting this value into the corresponding expressions.
Expression |
x=6 |
Side length
|
2x |
2⋅6 |
12
|
2x+3 |
2⋅6+3 |
15
|
2x+4 |
2⋅6+4 |
16
|
3x+1 |
3⋅6+1 |
19
|
Therefore, △ABC's side lengths are 12, 15 and 16, and the side lengths of △PQR are 12, 12 and 19.