The area of a rectangular sheet of metal is 24000mmsquare.the length is 10mm quarter than the width. Calculate the length and width
not quite sure what "10mm quarter than the width" means.
But if it is 10 mm greater, then
w(w+10) = 24000
now finish it off
Let's start by assigning variables to the unknowns. Let's say the width is represented by "w" and the length is represented by "l".
According to the given information, the area of the rectangular sheet is 24000 mm².
We can write the equation for the area of a rectangle:
Area = Length × Width
Substituting the given values, we have:
24000 = l × w
We are also told that the length is 10 mm less than the width:
l = w - 10
Now, we can substitute this expression for the length in terms of the width:
24000 = (w - 10) × w
Expanding the equation:
24000 = w² - 10w
Rearranging the equation into a quadratic form:
w² - 10w - 24000 = 0
To solve this quadratic equation, we can factor it or use the quadratic formula:
Using the quadratic formula:
w = [-(-10) ± √((-10)² - 4(1)(-24000))] / (2(1))
Simplifying further:
w = [10 ± √(100 + 96000)] / 2
w = [10 ± √96100] / 2
w = [10 ± 310] / 2
We have two possible solutions for w:
Solution 1: w = (10 + 310) / 2 = 320 / 2 = 160
Solution 2: w = (10 - 310) / 2 = -300 / 2 = -150
Since the width of a rectangle cannot be negative, we discard Solution 2.
Now let's calculate the length using the equation l = w - 10:
l = 160 - 10 = 150
Therefore, the length of the rectangular sheet is 150 mm and the width is 160 mm.
To calculate the length and width of the rectangular sheet of metal, we can set up a system of equations based on the given information.
Let's denote the width as 'W' and the length as 'L'.
Given:
Area = 24000 mm²
Length (L) = Width (W) - 10
The formula for the area of a rectangle is:
Area = Length × Width
So, we have the equation:
24000 = L × W
Substituting the second given condition, we get:
24000 = (W - 10) × W
Now, let's solve this equation to find the width and length.
Expanding the equation:
24000 = W² - 10W
Rearranging the equation:
W² - 10W - 24000 = 0
Now, we can use the quadratic formula to solve for W:
W = (-b ± √(b² - 4ac)) / (2a)
In our case, a = 1, b = -10, and c = -24000.
W = (-(-10) ± √((-10)² - 4(1)(-24000))) / (2(1))
W = (10 ± √(100 + 96000)) / 2
W = (10 ± √96100) / 2
W = (10 ± 310) / 2
Now, we have two possible values for the width: W1 and W2.
W1 = (10 + 310) / 2 = 320 / 2 = 160 mm
W2 = (10 - 310) / 2 = -300 / 2 = -150 mm (this negative value does not make sense in this context)
So, the width of the rectangular sheet is 160 mm.
To find the length, we substitute this value back into the given equation:
Length (L) = Width (W) - 10
L = 160 - 10 = 150 mm
Therefore, the length of the rectangular sheet is 150 mm and the width is 160 mm.