The equation 3x² - 48x + 6856 represents the area of the gym and track together in terms of width.
<h3>What is the area of the rectangle?</h3>
It is defined as the area occupied by the rectangle in two-dimensional planner geometry.
The area of a rectangle can be calculated using the following formula:
Rectangle area = length x width
We have:
A rectangular building for a gym is three times as long as it is wide. Just inside the walls of the building, there is a 6ft rectangular track along the walls of the gym and has an area of 7000ft²
Let x be the width of the rectangle.
As the area of track along the walls of the gym is 7000ft²
(x - 12)(3x - 12) = 7000
After simplifying:
3x² - 48x + 6856 = 0
Thus, the equation 3x² - 48x + 6856 represents the area of the gym and track together in terms of width.
Learn more about the rectangle here:
brainly.com/question/15019502
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Pythagoras theorem: leg 1 squared + leg 2 squared = hypotenuse squared
In the diagram, the triangle has angles 90 and 45. So the other angle in the triangle must be 45 degrees as well. (180 - 90 -45 = 45)
This means it is an isosceles triangle (since two angles are the same), so the two legs have the same length.
So we can say that length of leg1 = x, and the length of leg2 also equals x
Now let's use pythagoras' theorem:
leg1 = x
leg2 = x
hypotenuse = 16
x^2 + x^2 = 16^2
2x^2 = 16^2
2x^2 = 256
x^2 = 128
x = √(128)
x = 8√2
Answer: 2184
because when you multiply 14 times 12 times 13 you get 2184
Because it's a straight line
