the length of a rectangle is four times its width. if the area is 100 m2 what is the length of the rectangle?
L = Length
W = With
A = Area
L = 4 W
A = L * W
A = 4 W * W
A = 4 W ^ 2
100 = 4 W ^ 2 Divide both sides with 4
25 = W ^ 2
W = sqrt ( 25 )
W = 5 m
L = 4 W = 4 * 5 = 20 m
A = L * W = 20 * 5 = 100 m ^ 2
To find the length of the rectangle, we can use the formula for the area of a rectangle, which is length multiplied by width.
Let's break down the problem:
1. Let's assume the width of the rectangle is "w" (in meters).
2. According to the problem, the length of the rectangle is four times its width. So, the length would be 4w (in meters).
Now, we can use the formula for the area of a rectangle:
Area = Length × Width
We know that the area is given as 100 m². So, we can substitute the values into the formula and solve for the length:
100 m² = (4w) × w
100 m² = 4w²
To solve for w, divide both sides of the equation by 4:
25 m² = w²
Now, take the square root of both sides of the equation to solve for w:
w = √25 m
This simplifies to:
w = 5 m
Since the width is 5 meters, we can substitute this value back into the earlier equation to find the length:
Length = 4w = 4 × 5 m = 20 m
Therefore, the length of the rectangle is 20 meters.