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

answer:

1. 0.04

2. 0.15

step-by-step explanation:

i just finished that assignment for properties of probability distributions.

a. 74 degrees

step-by-step explanation:

because the lines through the side and the box in the corners shows that these are congruent triangles and since they are mirrored the 37 degrees is also mirrored so the answer is 37 * 2 which is 74.