Answer:
Maximum area =18
The area of the quadrilateral as a function of x and y = xy/2
Step-by-step explanation:
As the quadrilateral has mutually perpendicular diagonals, it is a rhombus. The area of a rhombus is denoted by the formula xy/2.
So, the area of the quadrilateral is xy/2.
As the sum of the sides is 12
x + y = 12
y = 12- x
So, the area, as a function of x alone, becomes x(12- x)/2
To find the maximum area, we find the derivative of the area function with respect to x and equate it to 0.
d/dx(x(12 - x)/2) = 0
d/dx(12x - x^2) = 0
12- 2x = 0
x = 6
The maximum area will then be 6(12- 6)/2 = 36/2 = 18
So, the maximum area is 18.
The formula of a distance between two points:
We have the points (-1, 8) and (5, -2). Substitute:
The base and height of the triangle is 18 inches and 9 inches respectively.
Step-by-step explanation:
Given,
The base of a triangle is twice of the height.
Area = 81 sq inches
Let,
Base (b) = 2x
Height (h) = x
To find its height and base.
Formula
Area of the triangle = bh
According to the problem,
bh = 81
or, ×x×2x = 81
or,
or, x =
or, x = 9
So,
Base = 2×9 inches = 18 inches
Height = 9 inches
6 percent of 5000 is 300 so 300 times 12 is 3,600 so your final answer is 3,600