the area of the rectangular tabletop at the right is 3 square meters. If the width is 0.5 m shorter than the length, what are the dimension of the tableshop?
If the length is x, the width is x-.5 so
x(x-0.5)=3
Now just solve for x
the area of a table top is 3 square meters.what is the are in square centimetera (cm)3
Let's assume the length of the rectangular tabletop is represented by "L" meters.
According to the given information, the width of the tabletop is 0.5 meters shorter than the length. So, the width can be represented as "(L - 0.5)" meters.
The area of a rectangle is calculated by multiplying its length and width. The area of the tabletop is given as 3 square meters.
So, we can set up the following equation: L * (L - 0.5) = 3.
Now, let's solve the equation to find the dimensions of the tabletop:
L^2 - 0.5L = 3.
Rearranging the equation:
L^2 - 0.5L - 3 = 0.
This is a quadratic equation. We can solve it either through factoring or the quadratic formula. Let's use the quadratic formula:
L = [-(-0.5) ± √((-0.5)^2 - 4*1*(-3))] / (2*1).
L = [0.5 ± √(0.25 + 12)] / 2.
L = [0.5 ± √12.25] / 2.
L = [0.5 ± 3.5] / 2.
So, we have two possible solutions for length: L = (0.5 + 3.5) / 2 = 4 / 2 = 2 meters, and L = (0.5 - 3.5) / 2 = -3 / 2 = -1.5 meters.
Since the length of a tabletop cannot be negative, we'll consider the positive solution, L = 2 meters.
Now, we can find the width by substituting the value of L into the expression (L - 0.5):
Width = 2 - 0.5 = 1.5 meters.
Therefore, the dimensions of the tabletop are 2 meters (length) and 1.5 meters (width).
To find the dimensions of the rectangular tabletop, let's use a variable to represent the length.
Let's say the length of the tabletop is 'x' meters.
According to the given information, the width is 0.5 meters shorter than the length. So the width can be expressed as 'x - 0.5' meters.
The area of a rectangle is calculated by multiplying its length and width. In this case, the area is given as 3 square meters.
So, we can set up an equation: x * (x - 0.5) = 3
To solve this equation, we can multiply the terms: x^2 - 0.5x = 3
Rearranging the equation to isolate the x-terms, we get: x^2 - 0.5x - 3 = 0
Now, we can solve this quadratic equation using factoring, completing the square, or the quadratic formula.
By factoring, we can rewrite the equation as: (x - 2)(x + 1.5) = 0
Setting each factor to zero, we get two possible solutions for x: x - 2 = 0 or x + 1.5 = 0
Solving these equations, we find: x = 2 or x = -1.5
Since the length can't be negative, we discard x = -1.5 as a valid solution.
Therefore, the length of the rectangular tabletop is 2 meters.
The width, based on the given information, is 0.5 meters shorter than the length.
So, the width is: 2 - 0.5 = 1.5 meters.
Thus, the dimensions of the tabletop are 2 meters (length) and 1.5 meters (width).