Palo alto college is planning to construct a rectangular parking lot on land bordered on one side by a highway. the plan is to use 720 feet of fencing to fence off the other three sides. what dimensions should the lot have if the enclosed area is to be a maximum?

The length of the 3 sides has a total dimension of 720 ft. One dimension, the length l, only has one side enclosed. The other dimension, the width w, has 2 sides enclosed. So,

720 ft = l + 2w 

Rearranging in terms of l: 

l = 720 - 2w 

Then the area equals length times width, or: 

A = (720-2w)(w) = 720w - 2w^2 

To get the maximum area, we take the derivative of the Area equation and set the derivative equal to 0: dA/dw = 0 

dA/dw = 720 - 4w = 0 

720 - 4w = 0 
4w = 720

w = 180 ft

Calculating for l:

l = 720 – 2w

l = 720 – 2(180)

l = 360 ft

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.