A rectangle is 3 times as long as it is wide, it's area is 108 square centimeters. What is the length? what is the width?
L=Lenght
W=With
A=Area
L=3W
A=L*W=108
108=3W*W
3W^2=108 Divide with 3
W^2=108/3
W^2=36
W=sqroot(36)
W=6 cm
L=3W
L=3*6=18 cm
A=L*W=18*6=108 cm^2
Why did the rectangle decide to spill the beans? Because it couldn't handle the pressure of keeping its area a secret!
Let's solve this challenge step by step, my friend. Let's say the width of the rectangle is "w" centimeters. Since the length is 3 times the width, we can represent it as "3w" centimeters.
Now let's use the formula for the area of a rectangle: Area = Length × Width. We know that the area is 108 square centimeters. So we have:
108 = (3w) × w
Now, let's simplify and solve this equation:
108 = 3w^2
Dividing both sides of the equation by 3, we have:
36 = w^2
Taking the square root of both sides, we get:
w = √36
w = 6
Therefore, the width of the rectangle is 6 centimeters. Since the length is 3 times the width, the length would be:
3w = 3 × 6 = 18 centimeters
So, the length of the rectangle is 18 centimeters.
To find the length and width of the rectangle, we will set up an equation based on the given information.
Let's say the width of the rectangle is 'w' centimeters.
According to the given information, the length of the rectangle is 3 times the width. Therefore, the length is 3w centimeters.
The area of a rectangle is given by the formula: area = length × width.
We are told that the area of the rectangle is 108 square centimeters. So, we can set up the following equation:
108 = (3w) × w
Now, we solve the equation to find the value of 'w':
108 = 3w^2
Divide both sides of the equation by 3:
36 = w^2
Taking the square root of both sides:
√36 = √(w^2)
6 = w
Hence, the width of the rectangle is 6 centimeters.
Now that we know the width, we can find the length:
Length = 3w = 3 × 6 = 18 centimeters.
Therefore, the length of the rectangle is 18 centimeters and the width is 6 centimeters.