A 60,000 square meter rectangular yard is to be enclosed on three sides by wood fencing that costs $25.00 per meter and on the fourth side with a stone wall that will cost $40.00 per meter. What is the minimum cost of enclosing this yard as described?

And we can solve for y and we got:

And using condition (1) we can solve for x and we got:

So then the minimum cost for this case would be:

Explanation:

For this case the graph attached illustrate the problem for this case

We know that the total area is 60000, so then we have:

If we solve for x we got:

 (1)

Now we can define the cost function like this:

We can use the condition (1) and if we replace in the cost function we have:

Since we need to minimize the cost, we can derivate the function in terms of y and we got:

And we can solve for y and we got:

And using condition (1) we can solve for x and we got:

So then the minimum cost for this case would be:

bd = 9 cm

step-by-step explanation:

in a 30°-60°-90° triangle, the ratio of side lengths is 1 : √3 : 2. that is, the longest side (hypotenuse) is twice the length of the shortest side.

all of the triangles in your geometry are 30°-60°-90° triangles. ac is the hypotenuse of δacd, and the short side of δabc.

the short side ad of δacd will be half the length of ac, so 3 cm. the hypotenuse ab of δabc will be twice the length of ac, so 12 cm. segment bd is the difference of the lengths ab and ad, so is

bd = ab -ad

bd = 12 cm - 3 cm = 9 cm

comment on side length ratios

you can figure the ratios of side lengths in a 30°-60°-90° triangle by considering the trig ratios of the angles. or you can figure the length of the altitude of an equilateral triangle of side length 2 using the pythagorean theorem.