the dimensions of a door are 3ft by 7ft 6in. if the same amount is added to each dimension of the door, the area is increased by 18ft^2. Find the dimensions of the new door.
(3+x)(7.5+x) = 3*7.5+18
x = 3/2
new dimensions: 4'6" by 9'0"
check:
3*7.5 = 22.5
4.5*9 = 40.5
How did you get 3/2 or 1.5
To find the dimensions of the new door, we need to determine the amount that was added to each dimension. We can set up an equation to represent the given information.
Let's denote the original width of the door as 'w', the original height as 'h', and the amount added to each dimension as 'x'.
We know that the original dimensions of the door are 3 ft by 7 ft 6 in, which can also be expressed as 3 ft by 7.5 ft.
Therefore, the area of the original door is given by:
Area = width * height
Area = 3 ft * 7.5 ft
Area = 22.5 ft^2
According to the given information, when the same amount 'x' is added to each dimension, the area is increased by 18 ft^2. So, the new area is:
New Area = Area + 18 ft^2
New Area = 22.5 ft^2 + 18 ft^2
New Area = 40.5 ft^2
Now, let's determine the new dimensions of the door.
New Area = New Width * New Height
40.5 ft^2 = (3 ft + x) * (7.5 ft + x)
Expanding this equation, we get:
40.5 ft^2 = 22.5 ft^2 + 7.5 ft * x + 3 ft * x + x^2
Combining like terms, we get a quadratic equation:
x^2 + 10.5 ft * x + 18 ft^2 = 0
To solve this quadratic equation, we can use factoring, completing the square, or the quadratic formula. Once we solve for 'x', we can substitute it back into the expressions for 'w' and 'h' to determine the new dimensions of the door.