Question

What is the perimeter of triangle PQR? Show your work.

Answer 1

The perimeter of triangle PQR is 17 ft

Explanation:

Consider the triangles PQR and STU

1. PQ ≅ ST = 4 ft (Given)

2. ∠PQR ≅ ∠STU (Given)

3. QR ≅ TU = 6 ft (Given)

Therefore, the two triangles are congruent by SAS postulate.

Now, from CPCTE, PR = SU. Therefore,

`3y-2=y+4\\3y-y=4+2\\2y=6\\y=(6)/(2)=3`

Now, side PR is given by plugging in 3 for 'y'.

PR = 3(3) - 2 = 9 - 2 = 7 ft

Now, perimeter of a triangle PQR is the sum of all of its sides.

Therefore, Perimeter = PQ + QR + PR

= (4 + 6 + 7) ft

= 17 ft

Hence, the perimeter of triangle PQR is 17 ft.