Question

chris wants to place fencing around a portion of his backyard for his new dog. if the dimensions of the rectangular space are 17 ft by 16 ft, how much fencing will chris need to buy?

Explanation:

Step1: Identify the shape and fencing sides

The area is a rectangle, and from the diagram (with one side maybe a gate or no fencing), but assuming it's a rectangle with length \( l = 17 \) ft and width \( w = 16 \) ft, and we need to find the perimeter (assuming all sides are fenced, but wait, the diagram has a small segment missing, maybe one width? Wait, no, let's check. Wait, the problem says "place fencing around a portion", but the dimensions are 17 ft by 16 ft. Wait, maybe it's a rectangle, and the fencing is the perimeter. Wait, perimeter of a rectangle is \( P = 2(l + w) \). Wait, no, maybe one side is not fenced? Wait, the diagram shows a rectangle with a small horizontal segment at the top, maybe the length is 17, width 16, and fencing is \( 2 \times 17 + 16 \)? Wait, no, let's re-examine. Wait, the user's problem: "Chris wants to place fencing around a portion of his backyard for his new dog. If the dimensions of the rectangular space are 17 ft by 16 ft, how much fencing will Chris need to buy?" Wait, maybe it's a rectangle, and fencing is the perimeter. Wait, perimeter of rectangle is \( 2(l + w) \). So length \( l = 17 \), width \( w = 16 \).

Step2: Calculate the perimeter

Perimeter formula: \( P = 2(l + w) \)
Substitute \( l = 17 \), \( w = 16 \):
\( P = 2(17 + 16) = 2(33) = 66 \)? Wait, no, wait, maybe the diagram has one side open? Wait, the original diagram (as per the image) has a rectangle with a small segment at the top, maybe the length is 17, width 16, and fencing is \( 17 + 17 + 16 \) (if one width is open). Wait, that would be \( 17 \times 2 + 16 = 34 + 16 = 50 \)? No, that doesn't make sense. Wait, maybe I misread. Wait, the dimensions are 17 ft by 16 ft. Let's assume it's a rectangle, and fencing is the perimeter. So \( 2(17 + 16) = 2 \times 33 = 66 \) feet? Wait, no, maybe the length is 17, width 16, and the fencing is three sides? Wait, the diagram shows a rectangle with a small horizontal line at the top, maybe the top side (length) has a gate, so fencing is two lengths and one width? No, that's not right. Wait, maybe the correct approach is: if it's a rectangle, perimeter is \( 2(l + w) \). So \( l = 17 \), \( w = 16 \), so \( 2(17 + 16) = 66 \). Wait, but maybe the diagram has one side missing, like the width. Wait, the user's image: the rectangle has a small segment at the top (maybe the width is 16, length 17). Wait, maybe the fencing is \( 17 + 17 + 16 = 50 \)? No, that's confusing. Wait, let's check the standard problem: if it's a rectangular fence, sometimes one side is against a house, so fencing is three sides. But the diagram here: the rectangle has a small horizontal line at the top, maybe the top length is open. So length is 17, width is 16. So fencing needed: \( 17 + 16 + 17 = 50 \)? No, that's 50. Wait, no, 17 + 16 + 17 = 50? 17+16=33, 33+17=50. Or 16 + 17 + 16 = 49? No. Wait, maybe I made a mistake. Wait, the problem says "dimensions of the rectangular space are 17 ft by 16 ft". Let's assume it's a regular rectangle, and fencing is the perimeter. So perimeter \( P = 2(l + w) = 2(17 + 16) = 66 \) feet. Wait, but maybe the diagram has one side open. Wait, the image shows a rectangle with a small horizontal segment at the top, maybe the top side (length) is open, so fencing is two widths and one length? No, that would be \( 16 + 17 + 16 = 49 \). This is confusing. Wait, maybe the original problem is a rectangle with length 17 and width 16, and fencing is the perimeter. So let's calculate perimeter: \( 2(17 + 16) = 66 \). So I think that's it.

Step1: Determine the formula for perimeter of rectangle

The perimeter \( P \) of a rectangle is given by \( P = 2 \times (length + width) \).

Step2: Substitute the values

Given length \( l = 17 \) ft and width \( w = 16 \) ft.
Substitute into the formula:
\( P = 2 \times (17 + 16) \)
First, calculate the sum inside the parentheses: \( 17 + 16 = 33 \)
Then, multiply by 2: \( 2 \times 33 = 66 \)

Answer:

66 feet (assuming all sides are fenced; if there's a missing side, the answer would change, but based on the given dimensions and standard rectangle perimeter, it's 66)