Help me please a) The upper bound for the area of the rectangle.
b) The lower bound for the perimeter of the rectangle.

Answers:

Explanation:

Part (a)

The horizontal portion is shown to be 87.3 cm long. This is the result after rounding has occurred. Specifically, rounding to one decimal place (tenths). The question is: What could the number have been before rounding?

You have to think in reverse of the usual rounding process.

The values 87.25, 87.26, 8.27, ... 8.33, 87.34 all round to 87.3 when we round to one decimal digit. Note the hundredths digit is increasing by 1 each time. We can see that 87.34 is the largest possible value for the horizontal piece. After that, 87.35 will round to 87.4 which is just out of reach.  

Through similar logic/reasoning, the vertical side can be at most 51.84 cm.

The area of the rectangle could be 87.34*51.84 = 4527.7056 which is the upper bound for the area. This is the largest possible area, given the values in the diagram, since we made each value as large as possible.

In short, 4527.7056 square cm is the max area.

Part (b)

We use the idea of part (a), but we'll use the smallest possible values this time.

So we go with 87.25 for the horizontal portion and 51.75 for the vertical portion.

Compute the perimeter with these smallest dimensions.

P = 2*(length + width)

P = 2*(87.25 + 51.75)

P = 278

The smallest perimeter possible is 278 cm which is the lower bound of the perimeter. This is guaranteed to be the smallest perimeter possible because we made the sides as small as possible, while staying in the restrictions as discussed in the previous section.

step-by-step explanation:

equation

you are asked to write the equation

  expression = 0

using the given expression. when you do that, you have

  2x^2-2x-12 = 0

factoring

you can see that each of the coefficients is even, so a factor of 2 can be removed immediately.

  2(x^2 -x -6) = 0

if you multiply the binomials (x+a)(x+b), you get

  (x +a)(x +b) = x^2 +(a+b)x +ab

this tells you the coefficient of x is the sum of two factors of the constant term. here, that means -1 is the sum of two factors of -6. we want to know those factors so we can factor the trinomial.

  -6 = -1×6 = -2×3 = -3×2 = -6×1

the factor pair that sums to -1 is {-3, 2}, so our factorization is

  2(x -3)(x +2) = 0

solutions

the solutions to this equation are the values of x that make the product zero. a product is zero only when only of the factors of the product is zero. here, that means

  x - 3 = 0

  x = 3 . . . add 3 to both sides of the equation

or

  x +2 = 0

  x = -2 . . . add -2 to both sides of the equation

the solutions to the equation are x=3 or x=-2. both of these values of x satisfy the equation—they make it be true.

i think it might be a but you might want a second opinion