Question

the perimeters of the triangles shown are equal. find the side lengths of each triangle. ab = pq = bc = qr = help me solve this view an example get more help clear all check answer review progress question 5 of 7

Explanation:

Step1: Calculate perimeter of first triangle

The perimeter of $\triangle ABC$ is $(2x + 6)+(2x)+(2x + 5)=6x+11$.

Step2: Calculate perimeter of second triangle

The perimeter of $\triangle PQR$ is $(2x)+(2x)+(3x + 8)=7x + 8$.

Step3: Set perimeters equal

Since perimeters are equal, we have $6x+11 = 7x+8$.

Step4: Solve for x

Subtract $6x$ from both sides: $11=x + 8$. Then subtract 8 from both sides to get $x=3$.

Step5: Find side - lengths of $\triangle ABC$

$AB=2x + 6=2\times3+6 = 12$.
$BC=2x+5=2\times3 + 5=11$.
$AC = 2x=2\times3=6$.

Step6: Find side - lengths of $\triangle PQR$

$PQ=2x=2\times3 = 6$.
$QR=2x=2\times3=6$.
$PR=3x + 8=3\times3+8=17$.

Answer:

$\overline{AB}=12$
$\overline{BC}=11$
$\overline{AC}=6$
$\overline{PQ}=6$
$\overline{QR}=6$
$\overline{PR}=17$