Among all rectangles that have a perimeter of 210, find the dimensions of the one whose area is largest. write your answers as fractions reduced to lowest terms.

Let the length of the rectangle be  x units then the width = (210 - 2x) / 2

= 105 - x  units

Area A = x(105 - x) = 105x - x^2

Finding  the derivative:_

dA/dx = 105 - 2x  = 0   for  max/minm volume

x = 52.5

this is for a maximum area because  second derivative  is negative ( = -2).

width = 105 - 52.5 = 52.5

Dimension for maximum area = 52 1/2 * 52 1/2.  ( The rectangle is actually a square).

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it