A carpenter is building a rectangular room with a fixed perimeter of 180 ft. What are the dimensions of the largest room that can be built? What is its area?

45ft x 45ft

Step-by-step explanation:

we know that

Perimeter = 2(Length) + 2(Width)  

180 = 2L + 2W

90 = L + W

90 - L = W

Area = Length *Width

= L(90 - L) →  = 180L - L²

There are 2 different methods for solving (depending on which math course you are taking).

Calculus: find the derivative, set it equal to zero, and solve for L.

= 90L - L² → 0 = 90 - 2L → 2L = 90 → L = 45

Algebra: find the vertex.

= - L² + 90L → L = -b/2a → L = -90/2(-1) → L = 45

insert L it into the Perimeter equation to solve for W:

90 - L = W → 90 - 45 = W → W = 45

45ft x 45ft

water molecules will move from the side of higher water concentration to the side of lower concentration until both solutions are isotonic. at this point, equilibrium is reached. in an isotonic solution, the flow of water in and out of the cell is happening at the same rate.

hope this < 3

so a parallelogram is just like a square base times height. multiply 40 and 39 to get 1560 inches.

a triangle is base times height divided by two. so multiply 7.9 and 5 and then divide it by 2 to get 19.75inches.

the kite can be split into two separate triangles and added together to get the total area. 30 x 4 /2 which equals 60. make sure to double it for the two triangles making 120.