The perimeter of a rectangle is 80x. The base is 7 times the height. In terms of x, what are the dimensions of the rectangle. What is the area?
Thanks..
call the height h
then the base is 7h
the perimeter is 80 x
so
2 h + 14 h = 80 x
16 h = 80 x
h = 5 x
area = h (7h) so put in 5x for h and you have it
5,35
To find the dimensions of the rectangle in terms of x, let's break down the given information:
1. The perimeter of a rectangle is given by the formula: P = 2(l + w), where l is the length and w is the width of the rectangle.
2. The given expression, 80x, represents the perimeter of the rectangle.
So, we can write the equation as: 80x = 2(l + w).
We also know that the base (l) is 7 times the height (w), or l = 7w.
Replacing l with 7w in the equation above, we get:
80x = 2(7w + w)
80x = 2(8w)
80x = 16w
To find the value of w in terms of x, divide both sides of the equation by 16:
w = (80x) / 16
w = 5x
Now, substitute the value of w back into the equation for l:
l = 7w
l = 7(5x)
l = 35x
So, the dimensions of the rectangle are:
Width (w) = 5x
Length (l) = 35x
To find the area of the rectangle, use the formula: A = l * w
Area (A) = 35x * 5x
Area (A) = 175x^2
Therefore, in terms of x, the dimensions of the rectangle are width (w) = 5x and length (l) = 35x, and the area (A) = 175x^2.
To find the dimensions of the rectangle, we can start by setting up a system of equations based on the given information.
Let's assume the base (length) of the rectangle is represented by 'l', and the height is represented by 'h'.
According to the given information, the perimeter of the rectangle is 80x. The perimeter of a rectangle is calculated by adding the lengths of all four sides. Therefore, we can write the equation:
Perimeter = 2(l + h) = 80x
Since the base is 7 times the height, mathematically we can express this relationship as:
l = 7h
Now we can solve this system of equations to find the values of 'l' and 'h'.
Substituting the value of l from the second equation into the first equation:
2(7h + h) = 80x
Simplifying the equation:
2(8h) = 80x
16h = 80x
Dividing both sides of the equation by 16:
h = 5x
Now, substitute the value of 'h' back into the equation l = 7h:
l = 7(5x)
l = 35x
So, the dimensions of the rectangle are:
Height (h) = 5x
Base (l) = 35x
To find the area of the rectangle, we can use the formula:
Area = Length * Width
Substituting the values we found:
Area = (35x) * (5x)
Area = 175x^2
Therefore, in terms of 'x', the dimensions of the rectangle are a height of 5x and a base of 35x, and the area of the rectangle is 175x^2.