The area of a rectangular garden is 420sq.cm. its length is one less than thrice its width. what are the dimensions of the rectangular garden?
A = LW
420 =(3w -1) * w
Are you sure the area of the garden is 420 centimeters? That would make the length about the length of my forearm and hand and the width about the length of my hand.
L = 3 W - 1
w * (3 w - 1) = 420 ... 3 w^2 - w - 420 = 0
solve the quadratic for w
substitute back to find L
Must be a garden for a doll house:
12 cm by 35 cm.
To solve this problem, we can set up an equation based on the given information.
Let's assume:
Length of the rectangle = L cm
Width of the rectangle = W cm
We are given that the area of the rectangular garden is 420 sq.cm, so we have:
L * W = 420
We are also given that the length (L) is one less than three times the width (W), which can be written as:
L = 3W - 1
Now, we can substitute the value of L from the second equation into the first equation:
(3W - 1) * W = 420
Simplifying the equation:
3W^2 - W - 420 = 0
Now, we need to solve this quadratic equation to find the possible values of W. We can use the quadratic formula:
W = (-b ± √(b^2 - 4ac)) / 2a
Here, a = 3, b = -1, and c = -420. Substituting the values into the formula:
W = (-(-1) ± √((-1)^2 - 4 * 3 * -420)) / (2 * 3)
W = (1 ± √(1 + 5040)) / 6
W = (1 ± √5041) / 6
Now, we have two possible values of W. Let's calculate both:
W1 = (1 + √5041) / 6 ≈ 13.34
W2 = (1 - √5041) / 6 ≈ -12.34 (which is not a valid dimension)
Since the width cannot be negative, we disregard the second value. Therefore, the width of the rectangular garden is approximately 13.34 cm.
Now, we can use this width value to find the length using the equation L = 3W - 1:
L = 3(13.34) - 1 ≈ 39.02 cm
So, the dimensions of the rectangular garden are approximately 39.02 cm for the length and 13.34 cm for the width.