The length of a rectangle is 3 times the width .The perimeter is 120 meters.Find the length and width
L = 3 W
2 L + 2 W = 120
substituting ... 2 (3 W) + 2 W = 120
... 8 W = 120
solve for W , then substitute back to find L
Oh, it seems like we've got a rectangle with an identity crisis! If the length of the rectangle is 3 times the width, we can say that the width is "W" and the length is "L = 3W". Now, to find the length and width, we need to solve for both sides of the equation.
But hey, let's have some fun! Let's say the width is the age of a clown, "C", and the length is "L = 3C." We've got a clown rectangle here! Now, let's proceed with the equation.
The formula for the perimeter of a rectangle is P = 2(L + W). We know the perimeter is 120 meters, so we can substitute the values:
120 = 2(3C + C)
Multiplying everything out:
120 = 2(4C)
Now, let's simplify:
120 = 8C
Dividing both sides by 8:
15 = C
Fantastic! The clown's age, I mean, the width of the rectangle, is 15 meters. If the length is 3 times the width, then the length is 3 times 15, which is 45 meters. Therefore, the length and width of the rectangle are 45 meters and 15 meters, respectively.
Now, I hope this clown rectangle puts a smile on your face!
Let's assume the width of the rectangle is x meters.
According to the given information, the length of the rectangle is 3 times the width, which means the length is 3x meters.
The formula for calculating the perimeter, P, of a rectangle is given by:
P = 2(length + width)
Substituting the given information into the formula, we get:
120 = 2(3x + x)
Simplifying the equation:
120 = 2(4x)
60 = 4x
x = 15
Therefore, the width of the rectangle is 15 meters.
Now, we can calculate the length of the rectangle:
Length = 3 * Width
Length = 3 * 15
Length = 45
Hence, the length of the rectangle is 45 meters and the width is 15 meters.
To find the length and width of a rectangle given its perimeter and the relationship between its length and width, you can follow these steps:
1. Let's assign variables to the length and width of the rectangle. We'll call the width "w" and the length "l".
2. According to the problem, the length of the rectangle is said to be three times the width. So, we can express the relationship as l = 3w.
3. The perimeter of a rectangle is calculated by adding the lengths of all its sides. In this case, the perimeter is given as 120 meters. The formula for the perimeter is P = 2(l + w).
4. To solve the problem, we substitute the expression for the length (l) from step 2 into the perimeter formula from step 3. This gives us the equation 120 = 2(3w + w).
5. Simplifying the equation, we have 120 = 2(4w), which further simplifies to 120 = 8w.
6. To isolate the variable, divide both sides of the equation by 8: 120/8 = w, which gives us w = 15.
7. Now, substitute the value of w back into the expression for the length from step 2 to find the length: l = 3w = 3(15) = 45.
Therefore, the length of the rectangle is 45 meters and the width is 15 meters.