Get the answers you need at Westonci.ca, where our expert community is always ready to help with accurate information. Get quick and reliable solutions to your questions from knowledgeable professionals on our comprehensive Q&A platform. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.
Sagot :
Sure, let's calculate the perimeter of the rectangle step-by-step.
### Step 1: Understanding the problem
We are given a rectangle with:
- Diagonal \( d = 15 \) cm
- Length \( l = 12 \) cm
We need to find the perimeter of the rectangle.
### Step 2: Use the Pythagorean Theorem
In a rectangle, the diagonal forms a right-angled triangle with the length and the width. According to the Pythagorean theorem:
[tex]\[ d^2 = l^2 + w^2 \][/tex]
where \( w \) is the width of the rectangle.
Rearranging for \( w^2 \):
[tex]\[ w^2 = d^2 - l^2 \][/tex]
### Step 3: Substitute the known values
Substituting \( d = 15 \) cm and \( l = 12 \) cm, we get:
[tex]\[ w^2 = 15^2 - 12^2 \][/tex]
[tex]\[ w^2 = 225 - 144 \][/tex]
[tex]\[ w^2 = 81 \][/tex]
### Step 4: Calculate width \( w \)
Taking the square root of both sides:
[tex]\[ w = \sqrt{81} \][/tex]
[tex]\[ w = 9 \][/tex]
Now we have:
- Length \( l = 12 \) cm
- Width \( w = 9 \) cm
### Step 5: Calculate the perimeter
The formula for the perimeter \( P \) of a rectangle is given by:
[tex]\[ P = 2(l + w) \][/tex]
Substituting the values of \( l \) and \( w \):
[tex]\[ P = 2(12 + 9) \][/tex]
[tex]\[ P = 2(21) \][/tex]
[tex]\[ P = 42 \][/tex]
### Final Answer
The perimeter of the rectangle is [tex]\( 42 \)[/tex] cm.
### Step 1: Understanding the problem
We are given a rectangle with:
- Diagonal \( d = 15 \) cm
- Length \( l = 12 \) cm
We need to find the perimeter of the rectangle.
### Step 2: Use the Pythagorean Theorem
In a rectangle, the diagonal forms a right-angled triangle with the length and the width. According to the Pythagorean theorem:
[tex]\[ d^2 = l^2 + w^2 \][/tex]
where \( w \) is the width of the rectangle.
Rearranging for \( w^2 \):
[tex]\[ w^2 = d^2 - l^2 \][/tex]
### Step 3: Substitute the known values
Substituting \( d = 15 \) cm and \( l = 12 \) cm, we get:
[tex]\[ w^2 = 15^2 - 12^2 \][/tex]
[tex]\[ w^2 = 225 - 144 \][/tex]
[tex]\[ w^2 = 81 \][/tex]
### Step 4: Calculate width \( w \)
Taking the square root of both sides:
[tex]\[ w = \sqrt{81} \][/tex]
[tex]\[ w = 9 \][/tex]
Now we have:
- Length \( l = 12 \) cm
- Width \( w = 9 \) cm
### Step 5: Calculate the perimeter
The formula for the perimeter \( P \) of a rectangle is given by:
[tex]\[ P = 2(l + w) \][/tex]
Substituting the values of \( l \) and \( w \):
[tex]\[ P = 2(12 + 9) \][/tex]
[tex]\[ P = 2(21) \][/tex]
[tex]\[ P = 42 \][/tex]
### Final Answer
The perimeter of the rectangle is [tex]\( 42 \)[/tex] cm.
Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.