Four hundred eighty dollars are available to fence in a rectangular garden. the fencing for the north and south sides of the garden costs $10 per foot and the fencing for the east and west sides costs $15 per foot. find the dimensions of the largest possible garden. (give exact answers.)

The rectangle will be its largest when the cost of the north/south fencing is equal to the cost of the east/west fencing, and both are half the total.

The north and south dimensions will be ($480/2)/($10/ft)/2 = 12 ft.

The east and west dimensions will be ($480/2)/($15/ft)/2 = 8 ft.

The largest possible garden is 12 ft in the north-south direction by 8 ft in the east-west direction.

Let p represent the cost per foot in the x direction, and let q represent the cost per foot in the y direction. Then the total cost is

... C = 2px + 2qy

and the area is

... A = xy

In terms of x, the area is

... A = x(C -2px)/(2q)

This describes a downward-opening parabola whose vertex is at x=C/(4p). That is, the value of x will be C/(4p) and the cost in the x-direction will be

.. 2px = 2p(C/(4p)) = C/2

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.