Lily used 4 square pieces of paper and 1 rectangular piece of paper to make a la...

· 21:16 05/07/2024

Lily used 4 square pieces of paper and 1 rectangular piece of paper to make a large square. Given that the perimeter of the rectangular piece of paper is 36, calculate the perimeter of the largest square.

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Chinh nè

1 năm trước

To solve this problem, we need to find the perimeter of the largest square that Lily made using 4 square pieces and 1 rectangular piece of paper. Here's the step-by-step solution:

1. Understand the pieces of paper:
- Lily used 4 square pieces.
- She used 1 rectangular piece, and its perimeter is given as 36 units.

2. Calculate the dimensions of the rectangular piece:
- Let the dimensions of the rectangular piece be $a$ (length) and $b$ (width).
- According to the problem, the perimeter of the rectangular piece is 36:
$2(a + b) = 36$
$a + b = 18$

3. Determine the side length of the largest square:
- Lily used these pieces to form a large square.
- To form a large square with the maximum area, the side length of the large square should be equal to the longer dimension of the rectangular piece (since it would maximize the use of the paper).
- Without loss of generality, assume $a \geq b$ .
- Thus, the side length $s$ of the largest square is $a$ .

4. Calculate the perimeter of the largest square:
- The perimeter $P$ of a square is given by $4s$ :
$P = 4s = 4a$

5. Substitute $a + b = 18$ into $P = 4a$ :
- From $a + b = 18$ , we have $b = 18 - a$ .
- Therefore, $P = 4a$ .

6. Solve for $a$ :
- To maximize $P$ , we need to find the maximum value of $a$ .
- The maximum $a$ occurs when $b = 18 - a$ is minimized, which happens when $a$ is maximized.
- The maximum possible value of $a$ is 9 (since $a + b = 18$ ).

7. Calculate $P$ when $a = 9$ :
- $P = 4 \times 9 = 36$ .

Therefore, the perimeter of the largest square that Lily made is $\boxed{36}$ units.

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Thiên Kim(Sally)

1 năm trước

To solve this problem, we need to find the perimeter of the largest square that Lily made using 4 square pieces and 1 rectangular piece of paper. Here's the step-by-step solution:

1. Understand the pieces of paper:
- Lily used 4 square pieces.
- She used 1 rectangular piece, and its perimeter is given as 36 units.

2. Calculate the dimensions of the rectangular piece:
- Let the dimensions of the rectangular piece be a $𝑎$ (length) and b $𝑏$ (width).
- According to the problem, the perimeter of the rectangular piece is 36:
2(a+b)=36 $2 (𝑎+𝑏) = 36a + b = 18 𝑎 +𝑏= 183. Determine the side length of the largest square: - Lily used these pieces to form a large square. - To form a large square with the maximum area, the side length of the large square should be equal to the longer dimension of the rectangular piece (since it would maximize the use of the paper). - Without loss of generality, assume a ≥ b 𝑎 \geq𝑏. - Thus, the side lengths 𝑠of the largest square isa 𝑎.4. Calculate the perimeter of the largest square: - The perimeter P 𝑃 of a square is given by 4 s 4 𝑠:P = 4 s = 4 a 𝑃 = 4𝑠= 4𝑎5. Substitute a + b = 18 𝑎 +𝑏= 18intoP = 4 a 𝑃 = 4𝑎: - Froma + b = 18 𝑎 +𝑏= 18, we haveb = 18 - a 𝑏 = 18 -𝑎. - Therefore,P = 4 a 𝑃 = 4𝑎.6. Solve for a 𝑎 : - To maximize P 𝑃, we need to find the maximum value of a 𝑎 . - The maximum a 𝑎 occurs when b = 18 - a 𝑏 =18- 𝑎 is minimized, which happens when is maximized. - The maximum possible value of is 9 (since 47. Calculate P 𝑃 when a = 9 𝑏 6Therefore, the perimeter of the largest square that Lily made is 𝑏 7 units....Xem thêmCảm ơn 0 bình luậnĐăng nhập để
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