The following warm-up exercises involve skills that were covered in earlier sections. you will use these skills in the exercise set for this section.
1. the sum is s and the product is a maximum.
2. the product is 192 and the sum is a minimum.
3. the product is 192 and the sum of the first plus three times the second is a minimum.
4. the second number is the reciprocal of the first and the sum is a minimum.
5. the sum of the first and twice the second is 100 and the product is a maximum.

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step-by-step explanation:

what i would say the best answer is a. 40.5

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240