Sid has a rectangular wooden deck that measures 348 centimeters by 792 centimeters. He builds an addition to the deck that makes it 126 centimeters longer. What is the perimeter of his deck now?
The Correct Answer and Explanation is:
Let’s break this problem down step by step.
Step 1: Understanding the Initial Dimensions of the Deck
Sid’s original wooden deck is rectangular in shape. The dimensions of the deck are:
- Length = 792 cm
- Width = 348 cm
Step 2: Addition to the Deck
Sid adds an extension to the deck that makes it 126 centimeters longer. This means that the length of the deck increases by 126 cm, so the new length will be:792 cm+126 cm=918 cm792 \, \text{cm} + 126 \, \text{cm} = 918 \, \text{cm}792cm+126cm=918cm
Thus, the new dimensions of the deck are:
- New Length = 918 cm
- Width = 348 cm (the width stays the same)
Step 3: Calculating the Perimeter of the New Deck
The formula for the perimeter PPP of a rectangle is:P=2×(Length+Width)P = 2 \times (\text{Length} + \text{Width})P=2×(Length+Width)
Substitute the new dimensions of the deck into this formula:P=2×(918 cm+348 cm)P = 2 \times (918 \, \text{cm} + 348 \, \text{cm})P=2×(918cm+348cm)
First, calculate the sum inside the parentheses:918 cm+348 cm=1266 cm918 \, \text{cm} + 348 \, \text{cm} = 1266 \, \text{cm}918cm+348cm=1266cm
Now multiply by 2 to find the perimeter:P=2×1266 cm=2532 cmP = 2 \times 1266 \, \text{cm} = 2532 \, \text{cm}P=2×1266cm=2532cm
Final Answer:
The perimeter of Sid’s deck after the addition is 2532 cm.
Explanation of the Process:
We started with the original dimensions of Sid’s deck, which were given as a length of 792 cm and a width of 348 cm. The addition extended the length by 126 cm, resulting in a new length of 918 cm. We then used the formula for the perimeter of a rectangle, which requires adding the length and width and then multiplying by 2. After substituting the new values for the length and width, we calculated the perimeter to be 2532 cm. This is the total distance around the newly expanded deck.
