Question

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

Answer 1

PQR= 17 ft

Explanation:

1. PQ ≅ ST = 4 ft (Given)

2. ∠PQR ≅ ∠STU (Given)

3. QR ≅ TU = 6 ft (Given)

Which makes the two triangles congruent by SAS postulate.

Now, from CPCTE, PR = SU

3y-2=y+4

Solve for y and simplify

Subtract Y from both sides.

Add 2 to both sides

3y-y=4+2

Add

2y=6

Divide both sides by 2

Y=3

Now, side PR is given by plugging in 3 for Y. PR = 3(3) - 2 = 9 - 2 = 7 ft. The perimeter of a triangle PQR is the sum of all of its sides. Perimeter = PQ + QR + PR = (4 + 6 + 7) ft = 17 ft. The perimeter of triangle PQR is 17 ft.

Answer 2

You know that the two triangles are congruent because two sides and one angle are congruent.

According to CPCTC, corresponding parts of congruent triangles are congruent, which means that PR and SU are equal.

3y-2=y+4
3y=y+6
2y=6
y=3

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

7+4+6=17

The perimeter is 17 feet.

Hope this helps!