area 432 square ft. width is 3/4 of length, what is length
Thanks for helping me....but can you make it a bit more clear?
Let x = length
Let 3/4x = width
Area of rectangle is length times width.
A = l * w
Substituting:
432 = x (3/4x)
Solve for x:
432 = (3/4) x^2
x^2 = 432 * 4/3
x^2 = 576
x = 24 ft. (length)
3/4x = 18 ft. (width)
hope this helps `u`
To find the length, we can use the given information that the area is 432 square feet and the width is 3/4 of the length.
Let's start by setting up an equation to represent the given information.
Area = Length × Width
Since the width is 3/4 of the length, we can say that:
Width = (3/4) × Length
Now substitute the given area into the equation:
432 = Length × (3/4) × Length
To solve for the length, we need to re-arrange the equation and solve for Length.
Multiply 432 by 4 to both sides of the equation to get rid of the fraction:
432 × 4 = Length × 3 × Length
1728 = 3 × Length^2
Divide both sides of the equation by 3:
1728 / 3 = Length^2
576 = Length^2
Take the square root of both sides to solve for the Length:
Length = √576
Length = 24
Therefore, the length is 24 feet.
To find the length given the area and width of a rectangular area, we can use the formula for the area of a rectangle, which is length multiplied by width. In this case, we are given that the area is 432 square feet and the width is 3/4 of the length.
Let's set up the equation using the given information:
Area = Length × Width
Substituting the given values:
432 = Length × (3/4 × Length)
To simplify the equation, multiply the terms inside the parentheses:
432 = (3/4) × (Length × Length)
Next, distribute the (3/4) to both terms inside the parentheses:
432 = (3/4) × (Length^2)
Next, let's isolate Length^2 by dividing both sides of the equation by (3/4):
Length^2 = 432 ÷ (3/4)
To simplify the right side of the equation further, we can multiply 432 by the reciprocal of (3/4), which is (4/3):
Length^2 = 432 × (4/3)
Now, multiply the numbers on the right side of the equation:
Length^2 = 576
To solve for Length, we need to take the square root of both sides of the equation:
Length = √576
The square root of 576 is 24, so the length of the rectangular area is 24 feet.