The perimeter of a rectangle is 480 meters and its length is 1.5 times its width. find the dimensions of the rectangle.
2 w + 2(1.5) w = 480
P=2W+2L
L=1.5W
480=2W+2(1.5W)
solve for W, then go back and solve for L
This is Pre-Cal?
YES!!!
hows this pre calc
Well, well, well, let's solve this rectangle mystery, shall we? Let's call the width of the rectangle "W" (short for "Whopper") and the length "L" (short for "Loch Ness Monster").
Now, we know that the perimeter of a rectangle is found by adding up all the sides, so we can set up an equation:
2L + 2W = 480
But wait! We also know that the length is 1.5 times the width, so we can rewrite that equation as:
2(1.5W) + 2W = 480
Simplifying that equation, we get:
3W + 2W = 480
Combining like terms, we have:
5W = 480
Now, divide both sides by 5 to solve for W:
W = 480/5
W = 96
So, the width of our rectangle is 96 meters. Since the length is 1.5 times the width, we can find the length by multiplying the width by 1.5:
L = 1.5(96)
L = 144
And voila! The dimensions of the rectangle are 96 meters (width) and 144 meters (length).
To find the dimensions of the rectangle, we need to set up a system of equations based on the given information.
Let's assume the width of the rectangle is represented by 'w'. According to the given information, the length of the rectangle is 1.5 times its width, so the length would be 1.5w.
The perimeter of a rectangle is given by the formula: P = 2(length + width)
Substituting the values in the equation, we get:
480 = 2(1.5w + w)
Simplifying the equation, we have:
480 = 2(2.5w)
Dividing both sides of the equation by 2, we get:
240 = 2.5w
Now, let's solve for 'w':
w = 240 / 2.5
w = 96
Therefore, the width of the rectangle is 96 meters.
Now, we can find the length of the rectangle by multiplying the width by 1.5:
length = 1.5w
length = 1.5 * 96
length = 144
Therefore, the dimensions of the rectangle are width = 96 meters and length = 144 meters.