The Gilberts are designing a rectangular patio for their backyard. The patio has an area of 432 square feet. The width of the patio is 3/4 its length . What is the length of the patio ?
Represent the unknowns.
Let x = length
since the width is 3/4 of the length,
Let (3/4)x = width
Recall that the area of rectangle is just width multiplied by the length,
A = w * l
Substituting,
432 = (3/4)x * x
432 = (3/4)x^2
432 * 4/3 = x^2
576 = x^2
Get the square root of both sides,
x = 24 feet (length)
Note that you should only get the positive root since dimensions (length, width, etc.) cannot be negative.
Hope this helps~ :3
So, then what is the answer?????
24
To find the length of the patio, we can use the information given about the area and the relationship between the width and length.
Let's represent the length of the patio as "L" (in feet) and the width as "W" (in feet).
According to the problem, the area of the rectangular patio is 432 square feet, so we have the equation:
L * W = 432
Additionally, it is stated that the width is 3/4 of the length, which gives us another equation:
W = (3/4) * L
Now, since we are looking for the length (L), we can substitute the second equation into the first equation:
L * (3/4) * L = 432
Simplifying this equation, we have:
(3/4) * L^2 = 432
To solve for L, we can isolate it by multiplying both sides of the equation by (4/3):
L^2 = (432 * 4) / 3
L^2 = 576
Taking the square root of both sides, we get:
L = sqrt(576)
L = 24
Thus, the length of the patio is 24 feet.