Question

13
if $a = 3$, $c = 5$ and the perimeter of the triangle = 15, what is the length of $b$?
14
susan designs frames. she needs to create a frame for a picture which measures 8.5 x 11 inches. she wants the frame to be 1 inch wide all around. what is the perimeter of the outside of the frame?
15
tina wants to buy a carpet for her family room that measures 20 feet by 30 feet. to make sure there is enough carpet she wants to have the length and width be cut 1 foot longer then needed. if the carpet she wants costs $7.75/square foot, how much will it cost?
16
find the perimeter of the parallelogram.

Explanation:

Step1: Solve for side b of triangle

Perimeter formula: $a + b + c = 15$. Substitute $a=3, c=5$:
$3 + b + 5 = 15$
$b = 15 - 3 - 5$

Step2: Calculate frame dimensions

Add 2 inches (1in each side) to picture size:
Length: $11 + 2 = 13$ in, Width: $8.5 + 2 = 10.5$ in

Step3: Find frame perimeter

Perimeter formula: $2\times(length + width)$
$2\times(13 + 10.5)$

Step4: Calculate carpet dimensions

Add 2ft (1ft each side) to room size:
Length: $30 + 2 = 32$ ft, Width: $20 + 2 = 22$ ft

Step5: Find carpet area & cost

Area: $32\times22 = 704$ sq ft. Cost: $704\times7.75$

Step6: Find parallelogram side

Missing base segment: $8 - 5 = 3$ cm. Full base: $4 + 3 = 7$ cm

Step7: Calculate parallelogram perimeter

Perimeter formula: $2\times(base + side)$
$2\times(7 + 6)$

Answer:

1. Length of $b$: $7$
2. Frame perimeter: $47$ inches
3. Carpet cost: $\$5456$
4. Parallelogram perimeter: $26$ cm