The length of a rectangle is three times as long as its width. Its area is 675 square feet.
a. Write an equation that demonstrates the given information.
b. Find the dimensions of the rectangle.
w * 3w = 675
now solve for w, then 3w
a. Let's assume the width of the rectangle is x feet. According to the given information, the length is three times as long as the width, so the length would be 3x feet.
The formula for the area of a rectangle is length * width, so we can set up the equation as:
Area = Length * Width
675 = 3x * x
b. Now we can solve the equation to find the dimensions of the rectangle.
675 = 3x^2
Divide both sides of the equation by 3:
225 = x^2
Take the square root of both sides:
15 = x
So, the width of the rectangle is 15 feet.
Since the length is three times as long as the width, the length would be:
3 * 15 = 45 feet
Therefore, the dimensions of the rectangle are 15 feet by 45 feet.
a. To write an equation that demonstrates the given information, let's assume that the width of the rectangle is "w" feet. According to the given information, the length of the rectangle is three times as long as its width, so the length would be 3w feet.
The formula for the area of a rectangle is given by: Area = Length * Width. In this case, the area is given as 675 square feet, so we can write the equation as:
675 = (3w) * w
b. To find the dimensions of the rectangle, we can solve the equation we created in part a. Let's simplify it and solve for "w":
675 = 3w^2
Divide both sides of the equation by 3:
225 = w^2
Take the square root of both sides to isolate "w":
√225 = √(w^2)
w = ±15
Since we can't have a negative width for a physical rectangle, we take the positive value:
w = 15
Now that we have the width, we can find the length by multiplying it by 3:
length = 3w = 3 * 15 = 45
Therefore, the dimensions of the rectangle are width = 15 feet and length = 45 feet.