the length of a rectangle is 5 times its width. if the length is decreased by 3 meters, and the width is increased by 10 meters, the perimeter will be 374 meters. find the length of the original rectangle.
original:
width --- x
length --- 5x , (it said so)
new dimensions:
length = 5x - 3
width = x+10
perimeter = 2* width + 2*length
= 2(x+10) + 2(5x-3) = 374
2x + 20 + 10x - 6 = 374
12x = 360
x = 30
So the original rectangle had a width of 30 m and a length of 150 m
Thank you
Why did the rectangle go on a diet? It wanted to decrease its length by 3 meters!
Let's get down to business. Let's assume the original width of the rectangle is 'w'. According to the problem, the length would be 5 times the width, so the length would be 5w meters.
Now, if the length is decreased by 3 meters, we have (5w - 3) meters. And if the width is increased by 10 meters, we have (w + 10) meters.
The perimeter of a rectangle is given by the formula: P = 2(length + width).
So, the perimeter can be expressed as P = 2((5w - 3) + (w + 10)).
Given that the perimeter is 374 meters, we can solve the equation:
2((5w - 3) + (w + 10)) = 374.
Now, let me crunch some numbers here. *beep boop beep*
2(6w + 7) = 374.
12w + 14 = 374.
12w = 360.
w = 30.
So, the original width of the rectangle is 30 meters. We know that the length is 5 times the width, so the length would be 5 * 30 = 150 meters.
Therefore, the length of the original rectangle is 150 meters.
To solve this problem, we need to follow a step-by-step approach:
Step 1: Assign variables to the unknown quantities.
Let's assign the variable "x" to represent the width of the original rectangle.
Since the length of the rectangle is 5 times its width, the length can be represented as 5x.
Step 2: Write the equation for the perimeter of the modified rectangle.
The perimeter of a rectangle is calculated by summing the lengths of all four sides.
In this case, when the length is decreased by 3 meters and the width is increased by 10 meters, the new length (5x - 3) and new width (x + 10) are used to calculate the new perimeter of 374 meters.
The equation for the perimeter is:
Perimeter = 2(length + width)
So, we can write the equation as:
374 = 2((5x - 3) + (x + 10))
Step 3: Solve the equation.
First, simplify the equation by distributing the 2 to both terms inside the parentheses:
374 = 2(5x - 3 + x + 10)
374 = 2(6x + 7)
Next, simplify further by multiplying 2 with each term inside the parentheses:
374 = 12x + 14
Then, isolate the variable x by subtracting 14 from both sides of the equation:
374 - 14 = 12x
360 = 12x
Finally, divide both sides of the equation by 12 to solve for x:
x = 360 ÷ 12
x = 30
Step 4: Determine the length of the original rectangle.
The length of the original rectangle is 5 times its width, which is represented by 5x.
Substituting the value of x into the equation, we get:
Length = 5 * 30
Length = 150 meters
Therefore, the length of the original rectangle is 150 meters.